LMFDB - Embedded newform 76.8.f.a.27.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(27,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.27");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.20
Character	$\chi$	$=$	76.27
Dual form			76.8.f.a.31.20

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.19272 + 8.73297i) q^{2} +(27.5600 - 47.7352i) q^{3} +(-24.5296 - 125.628i) q^{4} +(-200.879 + 347.932i) q^{5} +(218.640 + 584.026i) q^{6} -1173.75i q^{7} +(1273.54 + 689.387i) q^{8} +(-425.602 - 737.165i) q^{9} +O(q^{10})$	\(q+(-7.19272 + 8.73297i) q^{2} +(27.5600 - 47.7352i) q^{3} +(-24.5296 - 125.628i) q^{4} +(-200.879 + 347.932i) q^{5} +(218.640 + 584.026i) q^{6} -1173.75i q^{7} +(1273.54 + 689.387i) q^{8} +(-425.602 - 737.165i) q^{9} +(-1593.62 - 4256.84i) q^{10} +6708.37i q^{11} +(-6672.90 - 2291.36i) q^{12} +(-4220.71 + 2436.83i) q^{13} +(10250.3 + 8442.46i) q^{14} +(11072.4 + 19178.0i) q^{15} +(-15180.6 + 6163.20i) q^{16} +(10868.8 - 18825.4i) q^{17} +(9498.88 + 1585.45i) q^{18} +(20121.4 - 22113.4i) q^{19} +(48637.4 + 16701.3i) q^{20} +(-56029.3 - 32348.5i) q^{21} +(-58584.0 - 48251.4i) q^{22} +(358.300 - 206.865i) q^{23} +(68006.7 - 41793.1i) q^{24} +(-41642.0 - 72126.0i) q^{25} +(9077.63 - 54386.8i) q^{26} +73628.9 q^{27} +(-147456. + 28791.7i) q^{28} +(175783. - 101489. i) q^{29} +(-247122. - 41246.7i) q^{30} +14237.5 q^{31} +(55366.7 - 176902. i) q^{32} +(320226. + 184882. i) q^{33} +(86225.1 + 230323. i) q^{34} +(408386. + 235781. i) q^{35} +(-82168.4 + 71549.8i) q^{36} +23693.7i q^{37} +(48388.5 + 334775. i) q^{38} +268636. i q^{39} +(-495686. + 304621. i) q^{40} +(11071.6 + 6392.21i) q^{41} +(685502. - 256628. i) q^{42} +(635397. + 366847. i) q^{43} +(842757. - 164554. i) q^{44} +341978. q^{45} +(-770.608 + 4616.95i) q^{46} +(603071. - 348183. i) q^{47} +(-124175. + 894507. i) q^{48} -554148. q^{49} +(929393. + 155124. i) q^{50} +(-599090. - 1.03765e6i) q^{51} +(409666. + 470464. i) q^{52} +(855536. - 493944. i) q^{53} +(-529592. + 642999. i) q^{54} +(-2.33406e6 - 1.34757e6i) q^{55} +(809169. - 1.49482e6i) q^{56} +(-501045. - 1.56994e6i) q^{57} +(-378063. + 2.26509e6i) q^{58} +(-72889.5 + 126248. i) q^{59} +(2.13768e6 - 1.86143e6i) q^{60} +(503751. + 872523. i) q^{61} +(-102406. + 124336. i) q^{62} +(-865248. + 499551. i) q^{63} +(1.14664e6 + 1.75592e6i) q^{64} -1.95803e6i q^{65} +(-3.91787e6 + 1.46672e6i) q^{66} +(716672. + 1.24131e6i) q^{67} +(-2.63160e6 - 903647. i) q^{68} -22804.7i q^{69} +(-4.99647e6 + 1.87051e6i) q^{70} +(-1.79971e6 + 3.11720e6i) q^{71} +(-33828.3 - 1.23221e6i) q^{72} +(2.75878e6 - 4.77834e6i) q^{73} +(-206916. - 170422. i) q^{74} -4.59060e6 q^{75} +(-3.27162e6 - 1.98536e6i) q^{76} +7.87396e6 q^{77} +(-2.34599e6 - 1.93222e6i) q^{78} +(3.67893e6 - 6.37209e6i) q^{79} +(905083. - 6.51987e6i) q^{80} +(2.96000e6 - 5.12687e6i) q^{81} +(-135458. + 50710.9i) q^{82} -458673. i q^{83} +(-2.68949e6 + 7.83232e6i) q^{84} +(4.36664e6 + 7.56324e6i) q^{85} +(-7.77389e6 + 2.91028e6i) q^{86} -1.11881e7i q^{87} +(-4.62467e6 + 8.54336e6i) q^{88} +(-9.83287e6 + 5.67701e6i) q^{89} +(-2.45975e6 + 2.98648e6i) q^{90} +(2.86023e6 + 4.95407e6i) q^{91} +(-34776.9 - 39938.1i) q^{92} +(392385. - 679631. i) q^{93} +(-1.29704e6 + 7.77098e6i) q^{94} +(3.65201e6 + 1.14430e7i) q^{95} +(-6.91855e6 - 7.51835e6i) q^{96} +(2.44613e6 + 1.41227e6i) q^{97} +(3.98583e6 - 4.83936e6i) q^{98} +(4.94518e6 - 2.85510e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−7.19272	+	8.73297i	−0.635752	+	0.771893i
$2$	−7.19272	+	8.73297i	−0.635752	+	0.771893i
$3$	27.5600	−	47.7352i	0.589324	−	1.02074i	−0.404997	−	0.914318i	$-0.632727\pi$
$3$	27.5600	−	47.7352i	0.589324	−	1.02074i	0.994321	−	0.106421i	$-0.0339392\pi$
$4$	−24.5296	−	125.628i	−0.191638	−	0.981466i
$5$	−200.879	+	347.932i	−0.718685	+	1.24480i	0.242836	+	0.970067i	$0.421922\pi$
$5$	−200.879	+	347.932i	−0.718685	+	1.24480i	−0.961521	+	0.274732i	$0.911411\pi$
$6$	218.640	+	584.026i	0.413237	+	1.10383i
$7$		−	1173.75i		−	1.29340i	−0.762745	−	0.646700i	$-0.776149\pi$
$7$		−	1173.75i		−	1.29340i	0.762745	−	0.646700i	$-0.223851\pi$
$8$	1273.54	+	689.387i	0.879421	+	0.476045i
$9$	−425.602	−	737.165i	−0.194606	−	0.337067i
$10$	−1593.62	−	4256.84i	−0.503946	−	1.34613i
$11$			6708.37i			1.51965i	0.650129	+	0.759824i	$0.274715\pi$
$11$			6708.37i			1.51965i	−0.650129	+	0.759824i	$0.725285\pi$
$12$	−6672.90	−	2291.36i	−1.11476	−	0.382789i
$13$	−4220.71	+	2436.83i	−0.532825	+	0.307626i	−0.742166	−	0.670216i	$-0.766201\pi$
$13$	−4220.71	+	2436.83i	−0.532825	+	0.307626i	0.209341	+	0.977843i	$0.432868\pi$
$14$	10250.3	+	8442.46i	0.998366	+	0.822282i
$15$	11072.4	+	19178.0i	0.847077	+	1.46718i
$16$	−15180.6	+	6163.20i	−0.926550	+	0.376172i
$17$	10868.8	−	18825.4i	0.536552	−	0.929336i	−0.462534	−	0.886601i	$-0.653060\pi$
$17$	10868.8	−	18825.4i	0.536552	−	0.929336i	0.999086	−	0.0427344i	$-0.0136069\pi$
$18$	9498.88	+	1585.45i	0.383900	+	0.0640763i
$19$	20121.4	−	22113.4i	0.673007	−	0.739636i
$19$	20121.4	−	22113.4i	0.673007	−	0.739636i
$20$	48637.4	+	16701.3i	1.35946	+	0.466814i
$21$	−56029.3	−	32348.5i	−1.32022	−	0.762232i
$22$	−58584.0	−	48251.4i	−1.17301	−	0.966119i
$23$	358.300	−	206.865i	0.00614044	−	0.00354519i	−0.496927	−	0.867793i	$-0.665538\pi$
$23$	358.300	−	206.865i	0.00614044	−	0.00354519i	0.503067	+	0.864247i	$0.332205\pi$
$24$	68006.7	−	41793.1i	1.00418	−	0.617114i
$25$	−41642.0	−	72126.0i	−0.533017	−	0.923213i
$26$	9077.63	−	54386.8i	0.101290	−	0.606858i
$27$	73628.9			0.719905
$28$	−147456.	+	28791.7i	−1.26943	+	0.247864i
$29$	175783.	−	101489.i	1.33840	−	0.772723i	0.351826	−	0.936065i	$-0.385561\pi$
$29$	175783.	−	101489.i	1.33840	−	0.772723i	0.986569	+	0.163342i	$0.0522275\pi$
$30$	−247122.	−	41246.7i	−1.67104	−	0.278911i
$31$	14237.5			0.0858358			0.0429179	−	0.999079i	$-0.486335\pi$
$31$	14237.5			0.0858358			0.0429179	+	0.999079i	$0.486335\pi$
$32$	55366.7	−	176902.i	0.298692	−	0.954350i
$33$	320226.	+	184882.i	1.55116	+	0.895565i
$34$	86225.1	+	230323.i	0.376233	+	1.00499i
$35$	408386.	+	235781.i	1.61002	+	0.929547i
$36$	−82168.4	+	71549.8i	−0.293526	+	0.255593i
$37$			23693.7i			0.0769000i	0.999261	+	0.0384500i	$0.0122420\pi$
$37$			23693.7i			0.0769000i	−0.999261	+	0.0384500i	$0.987758\pi$
$38$	48388.5	+	334775.i	0.143054	+	0.989715i
$39$			268636.i			0.725167i
$40$	−495686.	+	304621.i	−1.22461	+	0.752576i
$41$	11071.6	+	6392.21i	0.0250881	+	0.0144846i	0.512492	−	0.858692i	$-0.328723\pi$
$41$	11071.6	+	6392.21i	0.0250881	+	0.0144846i	−0.487403	+	0.873177i	$0.662056\pi$
$42$	685502.	−	256628.i	1.42770	−	0.534481i
$43$	635397.	+	366847.i	1.21872	+	0.703631i	0.964645	−	0.263552i	$-0.0848942\pi$
$43$	635397.	+	366847.i	1.21872	+	0.703631i	0.254079	+	0.967183i	$0.418228\pi$
$44$	842757.	−	164554.i	1.49148	−	0.291222i
$45$	341978.			0.559441
$46$	−770.608	+	4616.95i	−0.00116730	+	0.00699363i
$47$	603071.	−	348183.i	0.847278	−	0.489176i	−0.0124537	−	0.999922i	$-0.503964\pi$
$47$	603071.	−	348183.i	0.847278	−	0.489176i	0.859731	+	0.510746i	$0.170631\pi$
$48$	−124175.	+	894507.i	−0.162065	+	1.16745i
$49$	−554148.			−0.672883
$50$	929393.	+	155124.i	1.05149	+	0.175503i
$51$	−599090.	−	1.03765e6i	−0.632406	−	1.09536i
$52$	409666.	+	470464.i	0.404034	+	0.463996i
$53$	855536.	−	493944.i	0.789355	−	0.455735i	−0.0503802	−	0.998730i	$-0.516043\pi$
$53$	855536.	−	493944.i	0.789355	−	0.455735i	0.839736	+	0.542996i	$0.182710\pi$
$54$	−529592.	+	642999.i	−0.457681	+	0.555690i
$55$	−2.33406e6	−	1.34757e6i	−1.89166	−	1.09215i
$56$	809169.	−	1.49482e6i	0.615717	−	1.13744i
$57$	−501045.	−	1.56994e6i	−0.358356	−	1.12285i
$58$	−378063.	+	2.26509e6i	−0.254429	+	1.52436i
$59$	−72889.5	+	126248.i	−0.0462044	+	0.0800283i	−0.888203	−	0.459452i	$-0.848046\pi$
$59$	−72889.5	+	126248.i	−0.0462044	+	0.0800283i	0.841998	+	0.539480i	$0.181379\pi$
$60$	2.13768e6	−	1.86143e6i	1.27766	−	1.11254i
$61$	503751.	+	872523.i	0.284159	+	0.492178i	0.972405	−	0.233299i	$-0.0749523\pi$
$61$	503751.	+	872523.i	0.284159	+	0.492178i	−0.688246	+	0.725478i	$0.741619\pi$
$62$	−102406.	+	124336.i	−0.0545703	+	0.0662560i
$63$	−865248.	+	499551.i	−0.435962	+	0.251703i
$64$	1.14664e6	+	1.75592e6i	0.546762	+	0.837288i
$65$		−	1.95803e6i		−	0.884346i
$66$	−3.91787e6	+	1.46672e6i	−1.67744	+	0.627975i
$67$	716672.	+	1.24131e6i	0.291111	+	0.504219i	0.974073	−	0.226235i	$-0.0726418\pi$
$67$	716672.	+	1.24131e6i	0.291111	+	0.504219i	−0.682962	+	0.730454i	$0.739308\pi$
$68$	−2.63160e6	−	903647.i	−1.01493	−	0.348512i
$69$		−	22804.7i		−	0.00835705i
$70$	−4.99647e6	+	1.87051e6i	−1.74109	+	0.651804i
$71$	−1.79971e6	+	3.11720e6i	−0.596760	+	1.03362i	0.396536	+	0.918019i	$0.370212\pi$
$71$	−1.79971e6	+	3.11720e6i	−0.596760	+	1.03362i	−0.993296	+	0.115599i	$0.963121\pi$
$72$	−33828.3	−	1.23221e6i	−0.0106811	−	0.389065i
$73$	2.75878e6	−	4.77834e6i	0.830017	−	1.43763i	−0.0680074	−	0.997685i	$-0.521664\pi$
$73$	2.75878e6	−	4.77834e6i	0.830017	−	1.43763i	0.898024	−	0.439946i	$-0.145003\pi$
$74$	−206916.	−	170422.i	−0.0593585	−	0.0488893i
$75$	−4.59060e6			−1.25648
$76$	−3.27162e6	−	1.98536e6i	−0.854901	−	0.518791i
$77$	7.87396e6			1.96551
$78$	−2.34599e6	−	1.93222e6i	−0.559751	−	0.461026i
$79$	3.67893e6	−	6.37209e6i	0.839511	−	1.45408i	−0.0507932	−	0.998709i	$-0.516175\pi$
$79$	3.67893e6	−	6.37209e6i	0.839511	−	1.45408i	0.890304	−	0.455366i	$-0.150492\pi$
$80$	905083.	−	6.51987e6i	0.197639	−	1.42372i
$81$	2.96000e6	−	5.12687e6i	0.618863	−	1.07190i
$82$	−135458.	+	50710.9i	−0.0271304	+	0.0101567i
$83$		−	458673.i		−	0.0880500i	−0.999030	−	0.0440250i	$-0.985982\pi$
$83$		−	458673.i		−	0.0880500i	0.999030	−	0.0440250i	$-0.0140181\pi$
$84$	−2.68949e6	+	7.83232e6i	−0.495099	+	1.44183i
$85$	4.36664e6	+	7.56324e6i	0.771225	+	1.33580i
$86$	−7.77389e6	+	2.91028e6i	−1.31793	+	0.493390i
$87$		−	1.11881e7i		−	1.82154i
$88$	−4.62467e6	+	8.54336e6i	−0.723421	+	1.33641i
$89$	−9.83287e6	+	5.67701e6i	−1.47848	+	0.853600i	−0.999704	−	0.0243369i	$-0.992253\pi$
$89$	−9.83287e6	+	5.67701e6i	−1.47848	+	0.853600i	−0.478776	+	0.877937i	$0.658919\pi$
$90$	−2.45975e6	+	2.98648e6i	−0.355666	+	0.431828i
$91$	2.86023e6	+	4.95407e6i	0.397884	+	0.689155i
$92$	−34776.9	−	39938.1i	−0.00465622	−	0.00534724i
$93$	392385.	−	679631.i	0.0505851	−	0.0876159i
$94$	−1.29704e6	+	7.77098e6i	−0.161067	+	0.965003i
$95$	3.65201e6	+	1.14430e7i	0.437018	+	1.36932i
$96$	−6.91855e6	−	7.51835e6i	−0.798116	−	0.867308i
$97$	2.44613e6	+	1.41227e6i	0.272131	+	0.157115i	0.629856	−	0.776712i	$-0.283114\pi$
$97$	2.44613e6	+	1.41227e6i	0.272131	+	0.157115i	−0.357725	+	0.933827i	$0.616447\pi$
$98$	3.98583e6	−	4.83936e6i	0.427787	−	0.519394i
$99$	4.94518e6	−	2.85510e6i	0.512223	−	0.295732i
$100$	−8.03956e6	+	7.00061e6i	−0.803956	+	0.700061i
$101$	1.41522e6	+	2.45123e6i	0.136678	+	0.236733i	0.926237	−	0.376941i	$-0.123024\pi$
$101$	1.41522e6	+	2.45123e6i	0.136678	+	0.236733i	−0.789559	+	0.613674i	$0.789691\pi$
$102$	1.33709e7	+	2.23172e6i	1.24755	+	0.208228i
$103$	−1.96576e7			−1.77255			−0.886277	−	0.463156i	$-0.846717\pi$
$103$	−1.96576e7			−1.77255			−0.886277	+	0.463156i	$0.846717\pi$
$104$	−7.05516e6	+	193688.i	−0.615021	+	0.0168844i
$105$	2.25102e7	−	1.29963e7i	1.89765	−	1.09561i
$106$	−1.84003e6	+	1.10242e7i	−0.150056	+	0.899032i
$107$	1.32453e7			1.04525			0.522625	−	0.852563i	$-0.324953\pi$
$107$	1.32453e7			1.04525			0.522625	+	0.852563i	$0.324953\pi$
$108$	−1.80609e6	−	9.24982e6i	−0.137961	−	0.706562i
$109$	−2.04950e7	−	1.18328e7i	−1.51584	−	0.875174i	−0.999827	−	0.0185957i	$-0.994080\pi$
$109$	−2.04950e7	−	1.18328e7i	−1.51584	−	0.875174i	−0.516018	−	0.856578i	$-0.672586\pi$
$110$	2.85565e7	−	1.06906e7i	2.04565	−	0.765820i
$111$	1.13102e6	+	652996.i	0.0784948	+	0.0453190i
$112$	7.23406e6	+	1.78182e7i	0.486540	+	1.19840i
$113$			2.46728e6i			0.160859i	0.996760	+	0.0804293i	$0.0256291\pi$
$113$			2.46728e6i			0.160859i	−0.996760	+	0.0804293i	$0.974371\pi$
$114$	1.73141e7	+	6.91654e6i	1.09455	+	0.437242i
$115$			166219.i			0.0101915i
$116$	−1.70617e7	−	1.95938e7i	−1.01489	−	1.16551i
$117$	3.59269e6	+	2.07424e6i	0.207381	+	0.119732i
$118$	−578250.	−	1.54461e6i	−0.0323988	−	0.0865430i
$119$	−2.20963e7	−	1.27573e7i	−1.20200	−	0.693977i
$120$	880074.	+	3.20571e7i	0.0464927	+	1.69352i
$121$	−2.55151e7			−1.30933
$122$	−1.12431e7	−	1.87656e6i	−0.560564	−	0.0935629i
$123$	610267.	−	352338.i	0.0295701	−	0.0170723i
$124$	−349241.	−	1.78863e6i	−0.0164494	−	0.0842449i
$125$	2.07264e6			0.0949159
$126$	1.86092e6	−	1.11493e7i	0.0828763	−	0.496537i
$127$	5.77668e6	+	1.00055e7i	0.250245	+	0.433437i	0.963593	−	0.267373i	$-0.0861555\pi$
$127$	5.77668e6	+	1.00055e7i	0.250245	+	0.433437i	−0.713348	+	0.700810i	$0.752822\pi$
$128$	−2.35819e7	−	2.61625e6i	−0.993902	−	0.110267i
$129$	3.50230e7	−	2.02206e7i	1.43645	−	0.829333i
$130$	1.70994e7	+	1.40836e7i	0.682621	+	0.562225i
$131$	1.55553e7	+	8.98086e6i	0.604546	+	0.349035i	0.770828	−	0.637044i	$-0.219843\pi$
$131$	1.55553e7	+	8.98086e6i	0.604546	+	0.349035i	−0.166282	+	0.986078i	$0.553176\pi$
$132$	1.53713e7	−	4.47643e7i	0.581704	−	1.69404i
$133$	−2.59556e7	−	2.36175e7i	−0.956645	−	0.870467i
$134$	−1.59952e7	−	2.66973e6i	−0.574277	−	0.0958519i
$135$	−1.47905e7	+	2.56179e7i	−0.517385	+	0.896137i
$136$	2.68199e7	−	1.64820e7i	0.914261	−	0.561854i
$137$	2.27229e7	+	3.93572e7i	0.754990	+	1.30768i	0.945379	+	0.325972i	$0.105692\pi$
$137$	2.27229e7	+	3.93572e7i	0.754990	+	1.30768i	−0.190390	+	0.981709i	$0.560975\pi$
$138$	199153.	+	164028.i	0.00645075	+	0.00531302i
$139$	3.84308e7	−	2.21880e7i	1.21374	−	0.700756i	0.250171	−	0.968202i	$-0.419513\pi$
$139$	3.84308e7	−	2.21880e7i	1.21374	−	0.700756i	0.963573	+	0.267446i	$0.0861797\pi$
$140$	1.96031e7	−	5.70881e7i	0.603778	−	1.75832i
$141$		−	3.83836e7i		−	1.15313i
$142$	−1.42776e7	−	3.81380e7i	−0.418451	−	1.11776i
$143$	−1.63472e7	−	2.83141e7i	−0.467484	−	0.809705i
$144$	1.10042e7	+	8.56753e6i	0.307107	+	0.239104i
$145$			8.15475e7i			2.22138i
$146$	2.18860e7	+	5.84616e7i	0.582012	+	1.55466i
$147$	−1.52723e7	+	2.64524e7i	−0.396546	+	0.686838i
$148$	2.97658e6	−	581197.i	0.0754747	−	0.0147369i
$149$	−2.77575e7	+	4.80774e7i	−0.687430	+	1.19066i	0.285236	+	0.958457i	$0.407928\pi$
$149$	−2.77575e7	+	4.80774e7i	−0.687430	+	1.19066i	−0.972666	+	0.232207i	$0.925405\pi$
$150$	3.30189e7	−	4.00896e7i	0.798810	−	0.969868i
$151$	4.19103e7			0.990606			0.495303	−	0.868720i	$-0.335057\pi$
$151$	4.19103e7			0.990606			0.495303	+	0.868720i	$0.335057\pi$
$152$	4.08700e7	−	1.42908e7i	0.943957	−	0.330069i
$153$	−1.85032e7			−0.417664
$154$	−5.66351e7	+	6.87631e7i	−1.24958	+	1.51716i
$155$	−2.86001e6	+	4.95369e6i	−0.0616889	+	0.106848i
$156$	3.37481e7	−	6.58954e6i	0.711726	−	0.138969i
$157$	4.74481e7	−	8.21825e7i	0.978521	−	1.69485i	0.310732	−	0.950498i	$-0.399426\pi$
$157$	4.74481e7	−	8.21825e7i	0.978521	−	1.69485i	0.667789	−	0.744351i	$-0.267241\pi$
$158$	2.91858e7	+	7.79606e7i	0.588670	+	1.57244i
$159$		−	5.44523e7i		−	1.07430i
$160$	5.04278e7	+	5.47996e7i	0.973308	+	1.05769i
$161$	−242808.	−	420555.i	−0.00458534	−	0.00794205i
$162$	2.34824e7	+	6.27258e7i	0.433950	+	1.15916i
$163$			5.81966e7i			1.05255i	0.850316	+	0.526273i	$0.176411\pi$
$163$			5.81966e7i			1.05255i	−0.850316	+	0.526273i	$0.823589\pi$
$164$	531455.	−	1.54770e6i	0.00940834	−	0.0273989i
$165$	−1.28653e8	+	7.42779e7i	−2.22960	+	1.28726i
$166$	4.00557e6	+	3.29910e6i	0.0679652	+	0.0559780i
$167$	398171.	+	689652.i	0.00661549	+	0.0114584i	0.869314	−	0.494260i	$-0.164561\pi$
$167$	398171.	+	689652.i	0.00661549	+	0.0114584i	−0.862699	+	0.505718i	$0.831228\pi$
$168$	−4.90547e7	−	7.98229e7i	−0.798175	−	1.29881i
$169$	−1.94980e7	+	3.37715e7i	−0.310732	+	0.538204i
$170$	−9.74575e7	−	1.62665e7i	−1.52140	−	0.253935i
$171$	−2.48649e7	−	5.42124e6i	−0.380278	−	0.0829110i
$172$	3.05000e7	−	8.88220e7i	0.457036	−	1.33098i
$173$	−2.94663e6	−	1.70124e6i	−0.0432677	−	0.0249806i	0.478210	−	0.878245i	$-0.341286\pi$
$173$	−2.94663e6	−	1.70124e6i	−0.0432677	−	0.0249806i	−0.521478	+	0.853265i	$0.674619\pi$
$174$	9.77052e7	+	8.04727e7i	1.40603	+	1.15805i
$175$	−8.46580e7	+	4.88773e7i	−1.19408	+	0.689404i
$176$	−4.13450e7	−	1.01837e8i	−0.571648	−	1.40803i
$177$	4.01766e6	+	6.95880e6i	0.0544587	+	0.0943252i
$178$	2.11479e7	−	1.26703e8i	0.281059	−	1.68391i
$179$	1.25576e8			1.63651			0.818256	−	0.574853i	$-0.194941\pi$
$179$	1.25576e8			1.63651			0.818256	+	0.574853i	$0.194941\pi$
$180$	−8.38859e6	−	4.29619e7i	−0.107210	−	0.549072i
$181$	−9.45518e7	+	5.45895e7i	−1.18521	+	0.684281i	−0.957214	−	0.289382i	$-0.906550\pi$
$181$	−9.45518e7	+	5.45895e7i	−1.18521	+	0.684281i	−0.227995	+	0.973662i	$0.573217\pi$
$182$	−6.38366e7	−	1.06549e7i	−0.784910	−	0.131008i
$183$	5.55334e7			0.669847
$184$	598919.	−	16442.3i	0.00708770	−	0.000194581i
$185$	−8.24378e6	−	4.75955e6i	−0.0957250	−	0.0552669i
$186$	3.11289e6	+	8.31509e6i	0.0354705	+	0.0947483i
$187$	1.26288e8	+	7.29122e7i	1.41226	+	0.815370i
$188$	−5.85345e7	−	6.72215e7i	−0.642480	−	0.737829i
$189$		−	8.64220e7i		−	0.931125i
$190$	−1.26199e8	−	5.04132e7i	−1.33481	−	0.533220i
$191$			4.57973e7i			0.475580i	0.971317	+	0.237790i	$0.0764230\pi$
$191$			4.57973e7i			0.475580i	−0.971317	+	0.237790i	$0.923577\pi$
$192$	1.15421e8	−	6.34215e6i	1.17687	−	0.0646669i
$193$	−3.35181e7	−	1.93517e7i	−0.335606	−	0.193762i	0.322721	−	0.946494i	$-0.395402\pi$
$193$	−3.35181e7	−	1.93517e7i	−0.335606	−	0.193762i	−0.658327	+	0.752732i	$0.728736\pi$
$194$	−2.99276e7	+	1.12039e7i	−0.294284	+	0.110170i
$195$	−9.34670e7	−	5.39632e7i	−0.902687	−	0.521167i
$196$	1.35930e7	+	6.96163e7i	0.128950	+	0.660411i
$197$	−1.09257e8			−1.01816			−0.509081	−	0.860718i	$-0.670015\pi$
$197$	−1.09257e8			−1.01816			−0.509081	+	0.860718i	$0.670015\pi$
$198$	−1.06358e7	+	6.37220e7i	−0.0973734	+	0.583393i
$199$	4.68486e7	−	2.70480e7i	0.421415	−	0.243304i	−0.274267	−	0.961654i	$-0.588435\pi$
$199$	4.68486e7	−	2.70480e7i	0.421415	−	0.243304i	0.695683	+	0.718349i	$0.255102\pi$
$200$	−3.30985e6	−	1.20563e8i	−0.0292552	−	1.06563i
$201$	7.90058e7			0.686235
$202$	−3.15858e7	−	5.27194e6i	−0.269626	−	0.0450030i
$203$	−1.19122e8	−	2.06326e8i	−0.999440	−	1.73108i
$204$	−1.15663e8	+	1.00715e8i	−0.953865	+	0.830597i
$205$	−4.44811e6	+	2.56812e6i	−0.0360609	+	0.0208198i
$206$	1.41391e8	−	1.71669e8i	1.12691	−	1.36822i
$207$	−304987.	−	176084.i	−0.00238993	−	0.00137983i
$208$	4.90543e7	−	6.30056e7i	0.377968	−	0.485465i
$209$	1.48345e8	+	1.34982e8i	1.12399	+	1.02273i
$210$	−4.84134e7	+	2.90059e8i	−0.360743	+	2.16132i
$211$	−2.52424e7	+	4.37212e7i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$211$	−2.52424e7	+	4.37212e7i	−0.184988	+	0.320408i	0.758585	+	0.651574i	$0.225891\pi$
$212$	−8.30389e7	−	9.53626e7i	−0.598558	−	0.687389i
$213$	9.92001e7	+	1.71820e8i	0.703370	+	1.21827i
$214$	−9.52700e7	+	1.15671e8i	−0.664520	+	0.806821i
$215$	−2.55275e8	+	1.47383e8i	−1.75176	+	1.01138i
$216$	9.37692e7	+	5.07588e7i	0.633099	+	0.342707i
$217$		−	1.67113e7i		−	0.111020i
$218$	2.50750e8	−	9.38723e7i	1.63924	−	0.613677i
$219$	−1.52064e8	−	2.63382e8i	−0.978298	−	1.69446i
$220$	−1.12038e8	+	3.26277e8i	−0.709393	+	2.06589i
$221$			1.05942e8i			0.660231i
$222$	−1.38377e7	+	5.18037e6i	−0.0848847	+	0.0317779i
$223$	−1.38437e8	+	2.39780e8i	−0.835960	+	1.44793i	0.0572859	+	0.998358i	$0.481755\pi$
$223$	−1.38437e8	+	2.39780e8i	−0.835960	+	1.44793i	−0.893246	+	0.449568i	$0.851578\pi$
$224$	−2.07639e8	−	6.49867e7i	−1.23436	−	0.386328i
$225$	−3.54458e7	+	6.13940e7i	−0.207456	+	0.359325i
$226$	−2.15467e7	−	1.77465e7i	−0.124166	−	0.102266i
$227$	−1.73844e7			−0.0986438			−0.0493219	−	0.998783i	$-0.515706\pi$
$227$	−1.73844e7			−0.0986438			−0.0493219	+	0.998783i	$0.515706\pi$
$228$	−1.84938e8	+	1.01455e8i	−1.03336	+	0.566895i
$229$	−4.49477e7			−0.247334			−0.123667	−	0.992324i	$-0.539465\pi$
$229$	−4.49477e7			−0.247334			−0.123667	+	0.992324i	$0.539465\pi$
$230$	−1.45158e6	−	1.19557e6i	−0.00786674	−	0.00647927i
$231$	2.17006e8	−	3.75865e8i	1.15832	−	2.00627i
$232$	2.93831e8	−	8.06666e6i	1.54486	−	0.0424117i
$233$	8.97810e7	−	1.55505e8i	0.464985	−	0.805377i	−0.534216	−	0.845348i	$-0.679393\pi$
$233$	8.97810e7	−	1.55505e8i	0.464985	−	0.805377i	0.999201	+	0.0399710i	$0.0127265\pi$
$234$	−4.39555e7	+	1.64555e7i	−0.224263	+	0.0839565i
$235$			2.79770e8i			1.40625i
$236$	1.76482e7	+	6.06011e6i	0.0873995	+	0.0300116i
$237$	−2.02782e8	−	3.51229e8i	−0.989488	−	1.71384i
$238$	2.70342e8	−	1.01207e8i	1.29985	−	0.486620i
$239$		−	2.19486e8i		−	1.03996i	−0.854180	−	0.519978i	$-0.825940\pi$
$239$		−	2.19486e8i		−	1.03996i	0.854180	−	0.519978i	$-0.174060\pi$
$240$	−2.86284e8	−	2.22892e8i	−1.33677	−	1.04077i
$241$	2.07658e8	−	1.19891e8i	0.955628	−	0.551732i	0.0608031	−	0.998150i	$-0.480634\pi$
$241$	2.07658e8	−	1.19891e8i	0.955628	−	0.551732i	0.894825	+	0.446418i	$0.147300\pi$
$242$	1.83523e8	−	2.22823e8i	0.832408	−	1.01066i
$243$	−8.26418e7	−	1.43140e8i	−0.369469	−	0.639939i
$244$	9.72561e7	−	8.46877e7i	0.428600	−	0.373212i
$245$	1.11317e8	−	1.92806e8i	0.483591	−	0.837604i
$246$	−1.31252e6	+	7.86372e6i	−0.00562126	+	0.0336787i
$247$	−3.10399e7	+	1.42367e8i	−0.131063	+	0.601131i
$248$	1.81320e7	+	9.81516e6i	0.0754858	+	0.0408617i
$249$	−2.18948e7	−	1.26410e7i	−0.0898761	−	0.0518900i
$250$	−1.49079e7	+	1.81003e7i	−0.0603430	+	0.0732649i
$251$	−1.34903e8	+	7.78864e7i	−0.538473	+	0.310888i	−0.744460	−	0.667667i	$-0.767293\pi$
$251$	−1.34903e8	+	7.78864e7i	−0.538473	+	0.310888i	0.205987	+	0.978555i	$0.433960\pi$
$252$	8.39816e7	+	9.64452e7i	0.330584	+	0.379646i
$253$	1.38773e6	+	2.40361e6i	0.00538743	+	0.00933131i
$254$	−1.28928e8	−	2.15192e7i	−0.493661	−	0.0823963i
$255$	4.81377e8			1.81800
$256$	1.92465e8	−	1.87122e8i	0.716990	−	0.697084i
$257$	1.51993e8	−	8.77532e7i	0.558544	−	0.322476i	−0.194017	−	0.980998i	$-0.562152\pi$
$257$	1.51993e8	−	8.77532e7i	0.558544	−	0.322476i	0.752561	+	0.658522i	$0.228818\pi$
$258$	−7.53252e7	+	4.51296e8i	−0.273068	+	1.63603i
$259$	2.78105e7			0.0994624
$260$	−2.45983e8	+	4.80297e7i	−0.867956	+	0.169474i
$261$	−1.49628e8	−	8.63875e7i	−0.520919	−	0.300752i
$262$	−1.90315e8	+	7.12473e7i	−0.653759	+	0.244745i
$263$	3.86941e8	+	2.23400e8i	1.31159	+	0.757249i	0.982360	−	0.187000i	$-0.0598764\pi$
$263$	3.86941e8	+	2.23400e8i	1.31159	+	0.757249i	0.329233	+	0.944249i	$0.393210\pi$
$264$	2.80364e8	+	4.56214e8i	0.937796	+	1.52600i
$265$			3.96891e8i			1.31012i
$266$	3.92942e8	−	5.67961e7i	1.28010	−	0.185026i
$267$			6.25833e8i			2.01219i
$268$	1.38363e8	−	1.20483e8i	0.439086	−	0.382343i
$269$	−5.01183e8	−	2.89358e8i	−1.56987	−	0.906364i	−0.996183	−	0.0872891i	$-0.972180\pi$
$269$	−5.01183e8	−	2.89358e8i	−1.56987	−	0.906364i	−0.573686	−	0.819075i	$-0.694487\pi$
$270$	−1.17336e8	−	3.13427e8i	−0.362793	−	0.969088i
$271$	−1.93475e8	−	1.11703e8i	−0.590517	−	0.340935i	0.174785	−	0.984607i	$-0.444077\pi$
$271$	−1.93475e8	−	1.11703e8i	−0.590517	−	0.340935i	−0.765302	+	0.643671i	$0.777410\pi$
$272$	−4.89709e7	+	3.52767e8i	−0.147553	+	1.06291i
$273$	3.15311e8			0.937930
$274$	−5.07144e8	−	8.46467e7i	−1.48938	−	0.248590i
$275$	4.83848e8	−	2.79350e8i	1.40296	−	0.809998i
$276$	−2.86490e6	+	559392.i	−0.00820216	+	0.00160153i
$277$	2.73588e8			0.773424			0.386712	−	0.922201i	$-0.373611\pi$
$277$	2.73588e8			0.773424			0.386712	+	0.922201i	$0.373611\pi$
$278$	−8.26543e7	+	4.95207e8i	−0.230732	+	1.38239i
$279$	−6.05952e6	−	1.04954e7i	−0.0167041	−	0.0289324i
$280$	3.57549e8	+	5.81812e8i	0.973381	+	1.58391i
$281$	3.95002e8	−	2.28055e8i	1.06201	−	0.613150i	0.136021	−	0.990706i	$-0.456569\pi$
$281$	3.95002e8	−	2.28055e8i	1.06201	−	0.613150i	0.925987	+	0.377556i	$0.123235\pi$
$282$	3.35203e8	+	2.76083e8i	0.890095	+	0.733107i
$283$	−1.94186e8	−	1.12113e8i	−0.509291	−	0.294039i	0.223251	−	0.974761i	$-0.428333\pi$
$283$	−1.94186e8	−	1.12113e8i	−0.509291	−	0.294039i	−0.732542	+	0.680722i	$0.761666\pi$
$284$	4.35752e8	+	1.49630e8i	1.12882	+	0.387619i
$285$	6.46883e8	+	1.41038e8i	1.65527	+	0.360894i
$286$	3.64847e8	+	6.08961e7i	0.922210	+	0.153925i
$287$	7.50286e6	−	1.29953e7i	0.0187344	−	0.0324490i
$288$	−1.53970e8	+	3.44755e7i	−0.379807	+	0.0850426i
$289$	−3.10941e7	−	5.38566e7i	−0.0757767	−	0.131249i
$290$	−7.12152e8	−	5.86548e8i	−1.71467	−	1.41225i
$291$	1.34830e8	−	7.78443e7i	0.320746	−	0.185183i
$292$	−6.67964e8	−	2.29368e8i	−1.57005	−	0.539129i
$293$		−	2.19183e8i		−	0.509063i	−0.967065	−	0.254531i	$-0.918079\pi$
$293$		−	2.19183e8i		−	0.509063i	0.967065	−	0.254531i	$-0.0819212\pi$
$294$	−1.21159e8	−	3.23637e8i	−0.278060	−	0.742750i
$295$	−2.92839e7	−	5.07212e7i	−0.0664128	−	0.115030i
$296$	−1.63341e7	+	3.01748e7i	−0.0366079	+	0.0676274i
$297$			4.93930e8i			1.09400i
$298$	−2.20207e8	−	5.88213e8i	−0.482030	−	1.28759i
$299$	−1.00819e6	+	1.74623e6i	−0.00218119	+	0.00377792i
$300$	1.12606e8	+	5.76707e8i	0.240789	+	1.23319i
$301$	4.30587e8	−	7.45798e8i	0.910076	−	1.57630i
$302$	−3.01449e8	+	3.66001e8i	−0.629780	+	0.764642i
$303$	1.56014e8			0.322191
$304$	−1.69165e8	+	4.59707e8i	−0.345345	+	0.938476i
$305$	−4.04771e8			−0.816884
$306$	1.33088e8	−	1.61588e8i	0.265531	−	0.322392i
$307$	1.40605e8	−	2.43535e8i	0.277343	−	0.480372i	−0.693381	−	0.720571i	$-0.743880\pi$
$307$	1.40605e8	−	2.43535e8i	0.277343	−	0.480372i	0.970723	+	0.240200i	$0.0772129\pi$
$308$	−1.93145e8	−	9.89186e8i	−0.376666	−	1.92908i
$309$	−5.41762e8	+	9.38359e8i	−1.04461	+	1.80932i
$310$	−2.26892e7	−	6.06069e7i	−0.0432566	−	0.115546i
$311$		−	1.51590e8i		−	0.285766i	−0.989740	−	0.142883i	$-0.954363\pi$
$311$		−	1.51590e8i		−	0.285766i	0.989740	−	0.142883i	$-0.0456372\pi$
$312$	−1.85194e8	+	3.42118e8i	−0.345212	+	0.637727i
$313$	1.51018e8	+	2.61571e8i	0.278371	+	0.482153i	0.970980	−	0.239160i	$-0.0768721\pi$
$313$	1.51018e8	+	2.61571e8i	0.278371	+	0.482153i	−0.692609	+	0.721313i	$0.743539\pi$
$314$	3.76417e8	+	1.00548e9i	0.686144	+	1.83282i
$315$		−	4.01397e8i		−	0.723581i
$316$	−8.90753e8	−	3.05870e8i	−1.58801	−	0.545295i
$317$	6.54984e8	−	3.78155e8i	1.15484	−	0.666750i	0.204781	−	0.978808i	$-0.434352\pi$
$317$	6.54984e8	−	3.78155e8i	1.15484	−	0.666750i	0.950063	+	0.312058i	$0.101018\pi$
$318$	4.75530e8	+	3.91660e8i	0.829246	+	0.682990i
$319$	6.80823e8	+	1.17922e9i	1.17427	+	2.03389i
$320$	−8.41277e8	+	4.62266e7i	−1.43521	+	0.0788618i
$321$	3.65041e8	−	6.32270e8i	0.615991	−	1.06693i
$322$	5.41914e6	+	904502.i	0.00904555	+	0.00150978i
$323$	−1.97598e8	−	6.19139e8i	−0.326267	−	1.02230i
$324$	−7.16685e8	−	2.46098e8i	−1.17063	−	0.401976i
$325$	3.51518e8	+	2.02949e8i	0.568009	+	0.327940i
$326$	−5.08230e8	−	4.18592e8i	−0.812453	−	0.669159i
$327$	−1.12968e9	+	6.52222e8i	−1.78665	+	1.03152i
$328$	9.69343e6	+	1.57734e7i	0.0151677	+	0.0246812i
$329$	−4.08680e8	−	7.07855e8i	−0.632700	−	1.09587i
$330$	2.76698e8	−	1.65778e9i	0.423846	−	2.53939i
$331$	−6.26453e7			−0.0949490			−0.0474745	−	0.998872i	$-0.515117\pi$
$331$	−6.26453e7			−0.0949490			−0.0474745	+	0.998872i	$0.515117\pi$
$332$	−5.76219e7	+	1.12511e7i	−0.0864181	+	0.0168737i
$333$	1.74661e7	−	1.00841e7i	0.0259204	−	0.0149652i
$334$	−8.88664e6	−	1.48326e6i	−0.0130504	−	0.00217823i
$335$	−5.75856e8			−0.836868
$336$	1.04993e9	+	1.45750e8i	1.50998	+	0.209615i
$337$	−2.39504e8	−	1.38278e8i	−0.340885	−	0.196810i	0.319778	−	0.947492i	$-0.396392\pi$
$337$	−2.39504e8	−	1.38278e8i	−0.340885	−	0.196810i	−0.660663	+	0.750682i	$0.729725\pi$
$338$	−1.54682e8	−	4.13184e8i	−0.217887	−	0.582016i
$339$	1.17776e8	+	6.79982e7i	0.164195	+	0.0947978i
$340$	8.43039e8	−	7.34094e8i	1.16325	−	1.01292i
$341$			9.55105e7i			0.130440i
$342$	2.26190e8	−	1.78151e8i	0.305761	−	0.240823i
$343$		−	3.16203e8i		−	0.423093i
$344$	5.56302e8	+	9.05227e8i	0.736811	+	1.19896i
$345$	7.93450e6	+	4.58098e6i	0.0104029	+	0.00600609i
$346$	3.60511e7	−	1.34963e7i	0.0467899	−	0.0175166i
$347$	−2.81881e8	−	1.62744e8i	−0.362170	−	0.209099i	0.307862	−	0.951431i	$-0.400386\pi$
$347$	−2.81881e8	−	1.62744e8i	−0.362170	−	0.209099i	−0.670032	+	0.742332i	$0.733720\pi$
$348$	−1.40553e9	+	2.74439e8i	−1.78778	+	0.349075i
$349$	−1.39904e9			−1.76174			−0.880869	−	0.473360i	$-0.843041\pi$
$349$	−1.39904e9			−1.76174			−0.880869	+	0.473360i	$0.843041\pi$
$350$	1.82077e8	−	1.09088e9i	0.226995	−	1.36000i
$351$	−3.10767e8	+	1.79421e8i	−0.383583	+	0.221462i
$352$	1.18672e9	+	3.71420e8i	1.45027	+	0.453906i
$353$	−9.65648e8			−1.16844			−0.584221	−	0.811595i	$-0.698600\pi$
$353$	−9.65648e8			−1.16844			−0.584221	+	0.811595i	$0.698600\pi$
$354$	−8.96689e7	−	1.49665e7i	−0.107431	−	0.0179312i
$355$	−7.23049e8	−	1.25236e9i	−0.857765	−	1.48569i
$356$	9.54386e8	+	1.09602e9i	1.12111	+	1.28749i
$357$	−1.21795e9	+	7.03182e8i	−1.41674	+	0.817954i
$358$	−9.03229e8	+	1.09665e9i	−1.04042	+	1.26321i
$359$	−4.88141e8	−	2.81828e8i	−0.556819	−	0.321480i	0.195049	−	0.980794i	$-0.437514\pi$
$359$	−4.88141e8	−	2.81828e8i	−0.556819	−	0.321480i	−0.751868	+	0.659314i	$0.770847\pi$
$360$	4.35521e8	+	2.35755e8i	0.491984	+	0.266319i
$361$	−8.41337e7	−	8.89903e8i	−0.0941228	−	0.995561i
$362$	2.03356e8	−	1.21837e9i	0.225308	−	1.34989i
$363$	−7.03195e8	+	1.21797e9i	−0.771618	+	1.33648i
$364$	5.52207e8	−	4.80846e8i	0.600133	−	0.522578i
$365$	1.10836e9	+	1.91973e9i	1.19304	+	2.06641i
$366$	−3.99436e8	+	4.84972e8i	−0.425857	+	0.517050i
$367$	−4.60312e8	+	2.65761e8i	−0.486094	+	0.280647i	−0.722953	−	0.690897i	$-0.757216\pi$
$367$	−4.60312e8	+	2.65761e8i	−0.486094	+	0.280647i	0.236858	+	0.971544i	$0.423882\pi$
$368$	−4.16426e6	+	5.34861e6i	−0.00435583	+	0.00559465i
$369$		−	1.08822e7i		−	0.0112752i
$370$	1.00860e8	−	3.77586e7i	0.103518	−	0.0387534i
$371$	−5.79767e8	−	1.00419e9i	−0.589447	−	1.02095i
$372$	−9.50055e7	−	3.26233e7i	−0.0956860	−	0.0328570i
$373$		−	1.07586e9i		−	1.07344i	−0.843762	−	0.536718i	$-0.819664\pi$
$373$		−	1.07586e9i		−	1.07344i	0.843762	−	0.536718i	$-0.180336\pi$
$374$	−1.54509e9	+	5.78430e8i	−1.52723	+	0.571742i
$375$	5.71219e7	−	9.89380e7i	0.0559362	−	0.0968844i
$376$	1.00807e9	−	2.76748e7i	0.977983	−	0.0268489i
$377$	−4.94621e8	+	8.56708e8i	−0.475420	+	0.823452i
$378$	7.54721e8	+	6.21609e8i	0.718729	+	0.591965i
$379$	1.76295e9			1.66343			0.831713	−	0.555206i	$-0.187361\pi$
$379$	1.76295e9			1.66343			0.831713	+	0.555206i	$0.187361\pi$
$380$	1.34797e9	−	7.39485e8i	1.26020	−	0.691333i
$381$	6.36821e8			0.589902
$382$	−3.99947e8	−	3.29407e8i	−0.367097	−	0.302351i
$383$	7.75302e8	−	1.34286e9i	0.705140	−	1.22134i	−0.261502	−	0.965203i	$-0.584218\pi$
$383$	7.75302e8	−	1.34286e9i	0.705140	−	1.22134i	0.966641	−	0.256135i	$-0.0824490\pi$
$384$	−7.74803e8	+	1.05358e9i	−0.698284	+	0.949532i
$385$	−1.58171e9	+	2.73960e9i	−1.41258	+	2.44667i
$386$	4.10084e8	−	1.53522e8i	0.362926	−	0.135867i
$387$		−	6.24523e8i		−	0.547722i
$388$	1.17418e8	−	3.41943e8i	0.102052	−	0.297196i
$389$	3.82110e8	+	6.61834e8i	0.329128	+	0.570066i	0.982339	−	0.187110i	$-0.0599119\pi$
$389$	3.82110e8	+	6.61834e8i	0.329128	+	0.570066i	−0.653211	+	0.757176i	$0.726579\pi$
$390$	1.14354e9	−	4.28103e8i	0.976170	−	0.365445i
$391$		−	8.99352e6i		−	0.00760871i
$392$	−7.05728e8	−	3.82023e8i	−0.591747	−	0.320323i
$393$	8.57407e8	−	4.95024e8i	0.712546	−	0.411389i
$394$	7.85854e8	−	9.54138e8i	0.647299	−	0.785913i
$395$	1.47804e9	+	2.56003e9i	1.20669	+	2.09005i
$396$	−4.79983e8	−	5.51216e8i	−0.388412	−	0.446055i
$397$	−7.25280e8	+	1.25622e9i	−0.581753	+	1.00763i	0.413518	+	0.910496i	$0.364300\pi$
$397$	−7.25280e8	+	1.25622e9i	−0.581753	+	1.00763i	−0.995272	+	0.0971303i	$0.969034\pi$
$398$	−1.00759e8	+	6.03676e8i	−0.0801110	+	0.479969i
$399$	−1.84272e9	+	5.88102e8i	−1.45229	+	0.463498i
$400$	1.07668e9	+	8.38268e8i	0.841154	+	0.654897i
$401$	−1.24902e9	−	7.21123e8i	−0.967308	−	0.558476i	−0.0688938	−	0.997624i	$-0.521947\pi$
$401$	−1.24902e9	−	7.21123e8i	−0.967308	−	0.558476i	−0.898415	+	0.439148i	$0.855280\pi$
$402$	−5.68266e8	+	6.89955e8i	−0.436275	+	0.529700i
$403$	−6.00925e7	+	3.46944e7i	−0.0457354	+	0.0264053i
$404$	2.73228e8	−	2.37918e8i	0.206153	−	0.179512i
$405$	1.18920e9	+	2.05976e9i	0.889535	+	1.54072i
$406$	2.65865e9	+	4.43752e8i	1.97161	+	0.329078i
$407$	−1.58946e8			−0.116861
$408$	−4.76177e7	−	1.73450e9i	−0.0347103	−	1.26434i
$409$	7.05668e8	−	4.07417e8i	0.509998	−	0.294448i	−0.222835	−	0.974856i	$-0.571531\pi$
$409$	7.05668e8	−	4.07417e8i	0.509998	−	0.294448i	0.732833	+	0.680409i	$0.238198\pi$
$410$	9.56670e6	−	5.73170e7i	0.00685517	−	0.0410714i
$411$	2.50496e9			1.77973
$412$	4.82193e8	+	2.46953e9i	0.339688	+	1.73970i
$413$	1.48184e8	+	8.55541e7i	0.103509	+	0.0597607i
$414$	3.73142e6	−	1.39692e6i	0.00258448	−	0.000967542i
$415$	1.59587e8	+	9.21375e7i	0.109605	+	0.0632803i
$416$	1.97393e8	+	8.81572e8i	0.134433	+	0.600386i
$417$		−	2.44600e9i		−	1.65189i
$418$	−2.24579e9	+	3.24608e8i	−1.50402	+	0.217392i
$419$			5.58260e8i			0.370755i	0.982667	+	0.185378i	$0.0593508\pi$
$419$			5.58260e8i			0.370755i	−0.982667	+	0.185378i	$0.940649\pi$
$420$	−2.18485e9	−	2.50911e9i	−1.43896	−	1.65252i
$421$	8.21075e8	+	4.74048e8i	0.536285	+	0.309624i	0.743572	−	0.668656i	$-0.233130\pi$
$421$	8.21075e8	+	4.74048e8i	0.536285	+	0.309624i	−0.207287	+	0.978280i	$0.566463\pi$
$422$	−2.00254e8	−	5.34916e8i	−0.129714	−	0.346491i
$423$	−5.13337e8	−	2.96375e8i	−0.329770	−	0.190393i
$424$	1.43007e9	−	3.92603e7i	0.911126	−	0.0250135i
$425$	−1.81040e9			−1.14397
$426$	−2.21401e9	−	3.69538e8i	−1.38754	−	0.231593i
$427$	1.02412e9	−	5.91278e8i	0.636583	−	0.367531i
$428$	−3.24903e8	−	1.66398e9i	−0.200309	−	1.02588i
$429$	−1.80211e9			−1.10200
$430$	5.49029e8	−	3.28940e9i	0.333009	−	1.99516i
$431$	−4.56382e7	−	7.90476e7i	−0.0274573	−	0.0475574i	0.851970	−	0.523590i	$-0.175408\pi$
$431$	−4.56382e7	−	7.90476e7i	−0.0274573	−	0.0475574i	−0.879428	+	0.476033i	$0.842074\pi$
$432$	−1.11773e9	+	4.53790e8i	−0.667028	+	0.270808i
$433$	1.82341e9	−	1.05275e9i	1.07939	−	0.623184i	0.148656	−	0.988889i	$-0.452505\pi$
$433$	1.82341e9	−	1.05275e9i	1.07939	−	0.623184i	0.930731	+	0.365704i	$0.119172\pi$
$434$	1.45939e8	+	1.20200e8i	0.0856955	+	0.0705812i
$435$	3.89269e9	+	2.24745e9i	2.26745	+	1.30911i
$436$	−9.83790e8	+	2.86499e9i	−0.568460	+	1.65547i
$437$	2.63500e6	−	1.20856e7i	0.00151041	−	0.00692763i
$438$	3.39386e9	+	5.66464e8i	1.92990	+	0.322117i
$439$	−7.51096e6	+	1.30094e7i	−0.00423711	+	0.00733889i	−0.868136	−	0.496326i	$-0.834682\pi$
$439$	−7.51096e6	+	1.30094e7i	−0.00423711	+	0.00733889i	0.863899	+	0.503665i	$0.168015\pi$
$440$	−2.04351e9	−	3.32525e9i	−1.14365	−	1.86097i
$441$	2.35847e8	+	4.08499e8i	0.130947	+	0.226806i
$442$	−9.25190e8	−	7.62012e8i	−0.509627	−	0.419743i
$443$	8.85433e8	−	5.11205e8i	0.483886	−	0.279371i	−0.238149	−	0.971229i	$-0.576541\pi$
$443$	8.85433e8	−	5.11205e8i	0.483886	−	0.279371i	0.722034	+	0.691857i	$0.243207\pi$
$444$	5.42908e7	−	1.58105e8i	0.0294365	−	0.0857248i
$445$		−	4.56156e9i		−	2.45388i
$446$	−1.09825e9	−	2.93364e9i	−0.586180	−	1.56579i
$447$	1.52999e9	+	2.65002e9i	0.810238	+	1.40337i
$448$	2.06101e9	−	1.34587e9i	1.08295	−	0.707181i
$449$			9.78301e8i			0.510047i	0.966935	+	0.255024i	$0.0820832\pi$
$449$			9.78301e8i			0.510047i	−0.966935	+	0.255024i	$0.917917\pi$
$450$	−2.81200e8	−	7.51137e8i	−0.145469	−	0.388576i
$451$	−4.28813e7	+	7.42726e7i	−0.0220115	+	0.0381251i
$452$	3.09959e8	−	6.05215e7i	0.157877	−	0.0308266i
$453$	1.15505e9	−	2.00060e9i	0.583788	−	1.01115i
$454$	1.25041e8	−	1.51818e8i	0.0627130	−	0.0761424i
$455$	−2.29824e9			−1.14381
$456$	4.44199e8	−	2.34479e9i	0.219382	−	1.15805i
$457$	−3.90029e9			−1.91157			−0.955785	−	0.294066i	$-0.904991\pi$
$457$	−3.90029e9			−1.91157			−0.955785	+	0.294066i	$0.904991\pi$
$458$	3.23296e8	−	3.92527e8i	0.157243	−	0.190915i
$459$	8.00261e8	−	1.38609e9i	0.386267	−	0.669034i
$460$	2.08817e7	−	4.07729e6i	0.0100026	−	0.00195307i
$461$	1.93326e8	−	3.34850e8i	0.0919044	−	0.159183i	−0.816408	−	0.577475i	$-0.804038\pi$
$461$	1.93326e8	−	3.34850e8i	0.0919044	−	0.159183i	0.908312	+	0.418292i	$0.137371\pi$
$462$	1.72156e9	+	4.59860e9i	0.812222	+	2.16960i
$463$			3.84078e9i			1.79840i	0.437541	+	0.899198i	$0.355849\pi$
$463$			3.84078e9i			1.79840i	−0.437541	+	0.899198i	$0.644151\pi$
$464$	−2.04300e9	+	2.62404e9i	−0.949414	+	1.21943i
$465$	1.57644e8	+	2.73047e8i	0.0727095	+	0.125937i
$466$	7.12254e8	+	1.90256e9i	0.326050	+	0.870939i
$467$		−	1.25512e9i		−	0.570263i	−0.958488	−	0.285132i	$-0.907963\pi$
$467$		−	1.25512e9i		−	0.570263i	0.958488	−	0.285132i	$-0.0920373\pi$
$468$	1.72455e8	−	5.02222e8i	0.0777704	−	0.226483i
$469$	1.45699e9	−	8.41194e8i	0.652157	−	0.376523i
$470$	−2.44323e9	−	2.01231e9i	−1.08548	−	0.894030i
$471$	−2.61534e9	−	4.52989e9i	−1.15333	−	1.99763i
$472$	−1.79861e8	+	1.10533e8i	−0.0787302	+	0.0483832i
$473$	−2.46094e9	+	4.26248e9i	−1.06927	+	1.85203i
$474$	4.52583e9	+	7.55400e8i	1.95197	+	0.325801i
$475$	−2.43284e9	−	5.30427e8i	−1.04157	−	0.227090i
$476$	−1.06066e9	+	3.08884e9i	−0.450765	+	1.31272i
$477$	−7.28236e8	−	4.20447e8i	−0.307226	−	0.177377i
$478$	1.91677e9	+	1.57870e9i	0.802734	+	0.661154i
$479$	−2.83021e8	+	1.63402e8i	−0.117664	+	0.0679335i	−0.557677	−	0.830058i	$-0.688307\pi$
$479$	−2.83021e8	+	1.63402e8i	−0.117664	+	0.0679335i	0.440013	+	0.897992i	$0.354974\pi$
$480$	4.00566e9	−	8.96909e8i	1.65322	−	0.370173i
$481$	−5.77374e7	−	1.00004e8i	−0.0236565	−	0.0409742i
$482$	−4.46617e8	+	2.67581e9i	−0.181665	+	1.08841i
$483$	−2.67671e7			−0.0108090
$484$	6.25876e8	+	3.20540e9i	0.250917	+	1.28506i
$485$	−9.82749e8	+	5.67390e8i	−0.391153	+	0.225832i
$486$	1.84446e9	+	3.07856e8i	0.728855	+	0.121652i
$487$	−1.38918e8			−0.0545014			−0.0272507	−	0.999629i	$-0.508675\pi$
$487$	−1.38918e8			−0.0545014			−0.0272507	+	0.999629i	$0.508675\pi$
$488$	4.00399e7	+	1.45847e9i	0.0155964	+	0.568104i
$489$	2.77803e9	+	1.60390e9i	1.07438	+	0.620291i
$490$	8.83100e8	+	2.35892e9i	0.339097	+	0.905789i
$491$	−2.54604e9	−	1.46996e9i	−0.970688	−	0.560427i	−0.0712424	−	0.997459i	$-0.522696\pi$
$491$	−2.54604e9	−	1.46996e9i	−0.970688	−	0.560427i	−0.899446	+	0.437032i	$0.856030\pi$
$492$	−5.92330e7	−	6.80237e7i	−0.0224226	−	0.0257503i
$493$		−	4.41225e9i		−	1.65843i
$494$	−1.02002e9	−	1.29507e9i	−0.380685	−	0.483337i
$495$			2.29411e9i			0.850152i
$496$	−2.16134e8	+	8.77486e7i	−0.0795311	+	0.0322890i
$497$	3.65881e9	+	2.11242e9i	1.33688	+	0.771849i
$498$	2.67877e8	−	1.00284e8i	0.0971925	−	0.0363855i
$499$	−7.95058e6	−	4.59027e6i	−0.00286449	−	0.00165381i	0.498567	−	0.866851i	$-0.333860\pi$
$499$	−7.95058e6	−	4.59027e6i	−0.00286449	−	0.00165381i	−0.501432	+	0.865197i	$0.667193\pi$
$500$	−5.08411e7	−	2.60381e8i	−0.0181895	−	0.0931567i
$501$	4.38943e7			0.0155947
$502$	2.90141e8	−	1.73832e9i	0.102364	−	0.613291i
$503$	1.16897e9	−	6.74905e8i	0.409558	−	0.236458i	−0.281042	−	0.959695i	$-0.590680\pi$
$503$	1.16897e9	−	6.74905e8i	0.409558	−	0.236458i	0.690600	+	0.723237i	$0.257347\pi$
$504$	−1.44631e9	+	3.97061e7i	−0.503216	+	0.0138150i
$505$	−1.13715e9			−0.392914
$506$	−3.09722e7	−	5.16953e6i	−0.0106278	−	0.00177388i
$507$	1.07473e9	+	1.86148e9i	0.366244	+	0.634353i
$508$	1.11527e9	−	9.71142e8i	0.377447	−	0.328670i
$509$	1.91247e9	−	1.10417e9i	0.642810	−	0.371127i	−0.142886	−	0.989739i	$-0.545638\pi$
$509$	1.91247e9	−	1.10417e9i	0.642810	−	0.371127i	0.785696	+	0.618612i	$0.212305\pi$
$510$	−3.46241e9	+	4.20385e9i	−1.15580	+	1.40331i
$511$	−5.60859e9	−	3.23812e9i	−1.85943	−	1.07354i
$512$	2.49782e8	+	3.02671e9i	0.0822464	+	0.996612i
$513$	1.48151e9	−	1.62819e9i	0.484501	−	0.532468i
$514$	−3.26896e8	+	1.95853e9i	−0.106179	+	0.636151i
$515$	3.94879e9	−	6.83950e9i	1.27391	−	2.20647i
$516$	−3.39936e9	−	3.90386e9i	−1.08924	−	1.25089i
$517$	2.33574e9	+	4.04562e9i	0.743375	+	1.28756i
$518$	−2.00033e8	+	2.42868e8i	−0.0632335	+	0.0767743i
$519$	−1.62418e8	+	9.37720e7i	−0.0509974	+	0.0294434i
$520$	1.34984e9	−	2.49362e9i	0.420989	−	0.777713i
$521$			1.44646e9i			0.448101i	0.974578	+	0.224050i	$0.0719280\pi$
$521$			1.44646e9i			0.448101i	−0.974578	+	0.224050i	$0.928072\pi$
$522$	1.83065e9	−	6.85332e8i	0.563324	−	0.210889i
$523$	2.10475e9	+	3.64554e9i	0.643347	+	1.11431i	0.984681	+	0.174367i	$0.0557879\pi$
$523$	2.10475e9	+	3.64554e9i	0.643347	+	1.11431i	−0.341334	+	0.939942i	$0.610879\pi$
$524$	7.46678e8	−	2.17447e9i	0.226712	−	0.660229i
$525$			5.38822e9i			1.62513i
$526$	−4.73410e9	+	1.77229e9i	−1.41836	+	0.530987i
$527$	1.54745e8	−	2.68027e8i	0.0460554	−	0.0797703i
$528$	−6.00068e9	−	8.33010e8i	−1.77412	−	0.246281i
$529$	−1.70233e9	+	2.94852e9i	−0.499975	+	0.865982i
$530$	−3.46604e9	−	2.85472e9i	−1.01127	−	0.832911i
$531$	1.24088e8			0.0359665
$532$	−2.33032e9	+	3.84007e9i	−0.671004	+	1.10573i
$533$	−6.23069e7			−0.0178234
$534$	−5.46538e9	−	4.50144e9i	−1.55319	−	1.27925i
$535$	−2.66071e9	+	4.60848e9i	−0.751206	+	1.30113i
$536$	5.69635e7	+	2.07492e9i	0.0159779	+	0.582002i
$537$	3.46086e9	−	5.99438e9i	0.964436	−	1.67045i
$538$	6.13183e9	−	2.29555e9i	1.69766	−	0.635548i
$539$		−	3.71743e9i		−	1.02254i
$540$	3.58112e9	+	1.22970e9i	0.978679	+	0.336062i
$541$	−5.91876e8	−	1.02516e9i	−0.160709	−	0.278356i	0.774414	−	0.632679i	$-0.218045\pi$
$541$	−5.91876e8	−	1.02516e9i	−0.160709	−	0.278356i	−0.935123	+	0.354323i	$0.884711\pi$
$542$	2.36711e9	−	8.86166e8i	0.638588	−	0.239066i
$543$			6.01794e9i			1.61305i
$544$	−2.72847e9	−	2.96502e9i	−0.726647	−	0.789644i
$545$	8.23401e9	−	4.75391e9i	2.17883	−	1.25795i
$546$	−2.26795e9	+	2.75361e9i	−0.596291	+	0.723982i
$547$	−1.59796e9	−	2.76775e9i	−0.417456	−	0.723056i	0.578227	−	0.815876i	$-0.303745\pi$
$547$	−1.59796e9	−	2.76775e9i	−0.417456	−	0.723056i	−0.995683	+	0.0928207i	$0.970412\pi$
$548$	4.38696e9	−	3.82004e9i	1.13876	−	0.991598i
$549$	4.28795e8	−	7.42696e8i	0.110598	−	0.191561i
$550$	−1.04063e9	+	6.23472e9i	−0.266702	+	1.59789i
$551$	1.29274e9	−	5.92925e9i	0.329216	−	1.50997i
$552$	1.57213e7	−	2.90427e7i	0.00397834	−	0.00734937i
$553$	−7.47924e9	−	4.31814e9i	−1.88070	−	1.08582i
$554$	−1.96784e9	+	2.38924e9i	−0.491706	+	0.597001i
$555$	−4.54397e8	+	2.62346e8i	−0.112826	+	0.0651402i
$556$	−3.73012e9	−	4.28370e9i	−0.920367	−	1.05696i
$557$	1.53677e9	+	2.66176e9i	0.376804	+	0.652643i	0.990595	−	0.136825i	$-0.0436898\pi$
$557$	1.53677e9	+	2.66176e9i	0.376804	+	0.652643i	−0.613792	+	0.789468i	$0.710357\pi$
$558$	1.35240e8	+	2.25728e7i	0.0329524	+	0.00550004i
$559$	−3.57577e9			−0.865822
$560$	−7.65270e9	−	1.06234e9i	−1.84144	−	0.255627i
$561$	6.96097e9	−	4.01892e9i	1.66456	−	0.961034i
$562$	−8.49545e8	+	5.08988e9i	−0.201887	+	1.20957i
$563$	−5.39992e9			−1.27529			−0.637644	−	0.770331i	$-0.720091\pi$
$563$	−5.39992e9			−1.27529			−0.637644	+	0.770331i	$0.720091\pi$
$564$	−4.82205e9	+	9.41537e8i	−1.13176	+	0.220984i
$565$	−8.58446e8	−	4.95624e8i	−0.200237	−	0.115607i
$566$	2.37581e9	−	8.89423e8i	0.550750	−	0.206182i
$567$	−6.01767e9	−	3.47430e9i	−1.38640	−	0.800437i
$568$	−4.44096e9	+	2.72917e9i	−1.01685	+	0.624900i
$569$		−	2.99867e9i		−	0.682394i	−0.939992	−	0.341197i	$-0.889168\pi$
$569$		−	2.99867e9i		−	0.682394i	0.939992	−	0.341197i	$-0.110832\pi$
$570$	−5.88453e9	+	4.63476e9i	−1.33091	+	1.04825i
$571$		−	1.64057e9i		−	0.368782i	−0.982853	−	0.184391i	$-0.940969\pi$
$571$		−	1.64057e9i		−	0.368782i	0.982853	−	0.184391i	$-0.0590313\pi$
$572$	−3.15605e9	+	2.74819e9i	−0.705111	+	0.613989i
$573$	2.18615e9	+	1.26217e9i	0.485443	+	0.280271i
$574$	5.95220e7	+	1.58994e8i	0.0131367	+	0.0350905i
$575$	−2.98407e7	−	1.72285e7i	−0.00654592	−	0.00377929i
$576$	8.06390e8	−	1.59259e9i	0.175819	−	0.347236i
$577$	−7.72488e9			−1.67408			−0.837040	−	0.547142i	$-0.815716\pi$
$577$	−7.72488e9			−1.67408			−0.837040	+	0.547142i	$0.815716\pi$
$578$	6.93980e8	+	1.15831e8i	0.149486	+	0.0249504i
$579$	−1.84752e9	+	1.06666e9i	−0.395561	+	0.228377i
$580$	1.02446e10	−	2.00033e9i	2.18021	−	0.425700i
$581$	−5.38367e8			−0.113884
$582$	−2.89984e8	+	1.73738e9i	−0.0609738	+	0.365312i
$583$	3.31356e9	+	5.73925e9i	0.692556	+	1.19954i
$584$	6.80754e9	−	4.18353e9i	1.41431	−	0.869157i
$585$	−1.44339e9	+	8.33342e8i	−0.298084	+	0.172099i
$586$	1.91412e9	+	1.57652e9i	0.392942	+	0.323638i
$587$	8.19441e9	+	4.73104e9i	1.67219	+	0.965437i	0.966412	+	0.256999i	$0.0827337\pi$
$587$	8.19441e9	+	4.73104e9i	1.67219	+	0.965437i	0.705773	+	0.708438i	$0.250600\pi$
$588$	3.69777e9	+	1.26975e9i	0.750101	+	0.257572i
$589$	2.86478e8	−	3.14840e8i	0.0577681	−	0.0634872i
$590$	6.53578e8	+	1.09088e8i	0.131013	+	0.0218672i
$591$	−3.01112e9	+	5.21541e9i	−0.600028	+	1.03928i
$592$	−1.46029e8	−	3.59684e8i	−0.0289276	−	0.0712517i
$593$	3.00971e9	+	5.21297e9i	0.592697	+	1.02658i	0.993867	+	0.110578i	$0.0352703\pi$
$593$	3.00971e9	+	5.21297e9i	0.592697	+	1.02658i	−0.401170	+	0.916004i	$0.631396\pi$
$594$	−4.31348e9	−	3.55270e9i	−0.844452	−	0.695514i
$595$	8.87736e9	−	5.12534e9i	1.72772	−	0.997502i
$596$	6.72073e9	+	2.30779e9i	1.30033	+	0.446513i
$597$		−	2.98177e9i		−	0.573540i
$598$	−7.99820e6	−	2.13647e7i	−0.00152946	−	0.00408547i
$599$	−1.77365e9	−	3.07205e9i	−0.337190	−	0.584030i	0.646713	−	0.762733i	$-0.276143\pi$
$599$	−1.77365e9	−	3.07205e9i	−0.337190	−	0.584030i	−0.983903	+	0.178704i	$0.942810\pi$
$600$	−5.84630e9	−	3.16470e9i	−1.10497	−	0.598141i
$601$		−	1.63972e9i		−	0.308112i	−0.988062	−	0.154056i	$-0.950766\pi$
$601$		−	1.63972e9i		−	0.308112i	0.988062	−	0.154056i	$-0.0492337\pi$
$602$	3.41594e9	+	9.12461e9i	0.638150	+	1.70462i
$603$	6.10034e8	−	1.05661e9i	0.113304	−	0.196248i
$604$	−1.02804e9	−	5.26509e9i	−0.189838	−	0.972246i
$605$	5.12544e9	−	8.87751e9i	0.940994	−	1.62985i
$606$	−1.12216e9	+	1.36246e9i	−0.204834	+	0.248697i
$607$	2.62678e9			0.476720			0.238360	−	0.971177i	$-0.423390\pi$
$607$	2.62678e9			0.476720			0.238360	+	0.971177i	$0.423390\pi$
$608$	−2.79785e9	−	4.78385e9i	−0.504849	−	0.863207i
$609$	−1.31320e10			−2.35598
$610$	2.91141e9	−	3.53486e9i	0.519336	−	0.630547i
$611$	−1.69693e9	+	2.93916e9i	−0.300967	+	0.521290i
$612$	4.53877e8	+	2.32452e9i	0.0800403	+	0.409923i
$613$	−2.80358e9	+	4.85594e9i	−0.491587	+	0.851454i	−0.999953	−	0.00968708i	$-0.996916\pi$
$613$	−2.80358e9	+	4.85594e9i	−0.491587	+	0.851454i	0.508366	+	0.861141i	$0.330250\pi$
$614$	1.11545e9	+	2.97958e9i	0.194474	+	0.519476i
$615$			2.83109e8i			0.0490784i
$616$	1.00278e10	+	5.42821e9i	1.72851	+	0.935672i
$617$	1.35093e9	+	2.33989e9i	0.231545	+	0.401048i	0.958263	−	0.285888i	$-0.0922885\pi$
$617$	1.35093e9	+	2.33989e9i	0.231545	+	0.401048i	−0.726718	+	0.686936i	$0.758955\pi$
$618$	−4.29792e9	−	1.14805e10i	−0.732485	−	1.95660i
$619$		−	1.71641e9i		−	0.290873i	−0.989368	−	0.145437i	$-0.953541\pi$
$619$		−	1.71641e9i		−	0.290873i	0.989368	−	0.145437i	$-0.0464587\pi$
$620$	6.92475e8	+	2.37784e8i	0.116690	+	0.0400694i
$621$	2.63813e7	−	1.52312e7i	0.00442054	−	0.00255220i
$622$	1.32383e9	+	1.09035e9i	0.220581	+	0.181676i
$623$	6.66340e9	+	1.15413e10i	1.10405	+	1.91226i
$624$	−1.65566e9	−	4.07805e9i	−0.272787	−	0.671903i
$625$	2.83693e9	−	4.91371e9i	0.464803	−	0.805062i
$626$	−3.37053e9	−	5.62570e8i	−0.549146	−	0.0916572i
$627$	1.05318e10	−	3.36120e9i	1.70634	−	0.544575i
$628$	−1.14883e10	−	3.94489e9i	−1.85096	−	0.635588i
$629$	4.46042e8	+	2.57523e8i	0.0714659	+	0.0412609i
$630$	3.50539e9	+	2.88713e9i	0.558527	+	0.460018i
$631$	9.32245e9	−	5.38232e9i	1.47716	−	0.852838i	0.477492	−	0.878636i	$-0.341546\pi$
$631$	9.32245e9	−	5.38232e9i	1.47716	−	0.852838i	0.999667	+	0.0257984i	$0.00821280\pi$
$632$	9.07809e9	−	5.57889e9i	1.43049	−	0.879099i
$633$	1.39136e9	+	2.40991e9i	0.218035	+	0.377648i
$634$	−1.40870e9	+	8.43993e9i	−0.219536	+	1.31530i
$635$	−4.64165e9			−0.719390
$636$	−6.84071e9	+	1.33569e9i	−1.05439	+	0.205877i
$637$	2.33890e9	−	1.35036e9i	0.358529	−	0.206997i
$638$	−1.51951e10	−	2.53619e9i	−2.31649	−	0.386642i
$639$	3.06385e9			0.464531
$640$	5.64737e9	−	7.67934e9i	0.851563	−	1.15796i
$641$	−7.34863e9	−	4.24273e9i	−1.10206	−	0.636272i	−0.165295	−	0.986244i	$-0.552858\pi$
$641$	−7.34863e9	−	4.24273e9i	−1.10206	−	0.636272i	−0.936760	+	0.349972i	$0.886191\pi$
$642$	2.89596e9	+	7.73563e9i	0.431936	+	1.15378i
$643$	−5.30300e9	−	3.06169e9i	−0.786653	−	0.454174i	0.0521300	−	0.998640i	$-0.483399\pi$
$643$	−5.30300e9	−	3.06169e9i	−0.786653	−	0.454174i	−0.838783	+	0.544466i	$0.816732\pi$
$644$	−4.68774e7	+	4.08194e7i	−0.00691612	+	0.00602235i
$645$			1.62475e10i			2.38412i
$646$	6.82819e9	+	2.72768e9i	0.996533	+	0.398089i
$647$			2.65343e9i			0.385161i	0.981281	+	0.192580i	$0.0616856\pi$
$647$			2.65343e9i			0.385161i	−0.981281	+	0.192580i	$0.938314\pi$
$648$	7.30407e9	−	4.48868e9i	1.05451	−	0.648046i
$649$	−8.46921e8	−	4.88970e8i	−0.121615	−	0.0702143i
$650$	−4.30071e9	+	1.61004e9i	−0.614248	+	0.229954i
$651$	−7.97718e8	−	4.60563e8i	−0.113322	−	0.0654267i
$652$	7.31110e9	−	1.42754e9i	1.03304	−	0.201708i
$653$	3.19676e9			0.449277			0.224638	−	0.974442i	$-0.427880\pi$
$653$	3.19676e9			0.449277			0.224638	+	0.974442i	$0.427880\pi$
$654$	2.42964e9	−	1.45567e10i	0.339641	−	2.03489i
$655$	−6.24946e9	+	3.60813e9i	−0.868956	+	0.501692i
$656$	−2.07470e8	−	2.88009e7i	−0.0286941	−	0.00398329i
$657$	−4.69657e9			−0.646104
$658$	9.12120e9	+	1.52241e9i	1.24813	+	0.208324i
$659$	7.20835e8	+	1.24852e9i	0.0981154	+	0.169941i	0.910905	−	0.412617i	$-0.135385\pi$
$659$	7.20835e8	+	1.24852e9i	0.0981154	+	0.169941i	−0.812789	+	0.582558i	$0.802052\pi$
$660$	1.24872e10	+	1.43404e10i	1.69067	+	1.94159i
$661$	−2.59208e9	+	1.49654e9i	−0.349094	+	0.201550i	−0.664286	−	0.747478i	$-0.731264\pi$
$661$	−2.59208e9	+	1.49654e9i	−0.349094	+	0.201550i	0.315192	+	0.949028i	$0.397931\pi$
$662$	4.50590e8	−	5.47080e8i	0.0603641	−	0.0732905i
$663$	5.05717e9	+	2.91976e9i	0.673923	+	0.389090i
$664$	3.16203e8	−	5.84137e8i	0.0419158	−	0.0774330i
$665$	1.34312e10	−	4.28655e9i	1.77108	−	0.565239i
$666$	−3.75650e7	+	2.25063e8i	−0.00492747	+	0.0295219i
$667$	4.19888e7	−	7.27267e7i	0.00547889	−	0.00948972i
$668$	7.68723e7	−	6.69381e7i	0.00997821	−	0.00868873i
$669$	7.63064e9	+	1.32167e10i	0.985303	+	1.70659i
$670$	4.14197e9	−	5.02894e9i	0.532041	−	0.645973i
$671$	−5.85321e9	+	3.37935e9i	−0.747937	+	0.431822i
$672$	−8.82467e9	+	8.12065e9i	−1.12178	+	1.03228i
$673$			6.13083e9i			0.775294i	0.921808	+	0.387647i	$0.126712\pi$
$673$			6.13083e9i			0.775294i	−0.921808	+	0.387647i	$0.873288\pi$
$674$	2.93026e9	−	1.09699e9i	0.368635	−	0.138004i
$675$	−3.06605e9	−	5.31056e9i	−0.383722	−	0.664626i
$676$	4.72091e9	+	1.62108e9i	0.587776	+	0.201833i
$677$		−	9.57013e8i		−	0.118538i	−0.998242	−	0.0592690i	$-0.981123\pi$
$677$		−	9.57013e8i		−	0.118538i	0.998242	−	0.0592690i	$-0.0188770\pi$
$678$	−1.44096e9	+	5.39445e8i	−0.177561	+	0.0664727i
$679$	1.65765e9	−	2.87114e9i	0.203212	−	0.351974i
$680$	3.47075e8	+	1.26424e10i	0.0423294	+	1.54187i
$681$	−4.79114e8	+	8.29849e8i	−0.0581331	+	0.100690i
$682$	−8.34091e8	−	6.86980e8i	−0.100686	−	0.0829276i
$683$	−5.69717e9			−0.684205			−0.342103	−	0.939663i	$-0.611139\pi$
$683$	−5.69717e9			−0.684205			−0.342103	+	0.939663i	$0.611139\pi$
$684$	−7.11300e7	+	3.25670e9i	−0.00849878	+	0.389118i
$685$	−1.82582e10			−2.17040
$686$	2.76139e9	+	2.27436e9i	0.326583	+	0.268983i
$687$	−1.23876e9	+	2.14559e9i	−0.145760	+	0.252463i
$688$	−1.19067e10	−	1.65287e9i	−1.39390	−	0.193499i
$689$	−2.40731e9	+	4.16959e9i	−0.280392	+	0.485653i
$690$	−9.70762e7	+	3.63420e7i	−0.0112497	+	0.00421150i
$691$		−	4.91805e9i		−	0.567048i	−0.958965	−	0.283524i	$-0.908496\pi$
$691$		−	4.91805e9i		−	0.567048i	0.958965	−	0.283524i	$-0.0915036\pi$
$692$	−1.41443e8	+	4.11909e8i	−0.0162259	+	0.0472530i
$693$	−3.35118e9	−	5.80441e9i	−0.382499	−	0.662509i
$694$	3.44873e9	−	1.29109e9i	0.391653	−	0.146622i
$695$			1.78284e10i			2.01449i
$696$	7.71292e9	−	1.42484e10i	0.867134	−	1.60190i
$697$	2.40672e8	−	1.38952e8i	0.0269222	−	0.0155435i
$698$	1.00629e10	−	1.22178e10i	1.12003	−	1.35987i
$699$	−4.94872e9	−	8.57143e9i	−0.548053	−	0.949256i
$700$	8.21697e9	+	9.43643e9i	0.905458	+	1.03984i
$701$	−2.82998e8	+	4.90167e8i	−0.0310292	+	0.0537441i	−0.881123	−	0.472887i	$-0.843212\pi$
$701$	−2.82998e8	+	4.90167e8i	−0.0310292	+	0.0537441i	0.850094	+	0.526631i	$0.176545\pi$
$702$	6.68376e8	−	4.00444e9i	0.0729190	−	0.436880i
$703$	5.23948e8	+	4.76749e8i	0.0568780	+	0.0517542i
$704$	−1.17794e10	+	7.69210e9i	−1.27238	+	0.830885i
$705$	1.33549e10	+	7.71045e9i	1.43542	+	0.828740i
$706$	6.94563e9	−	8.43297e9i	0.742840	−	0.901912i
$707$	2.87714e9	−	1.66111e9i	0.306191	−	0.176779i
$708$	7.75665e8	−	6.75426e8i	0.0821406	−	0.0715256i
$709$	−6.64388e9	−	1.15075e10i	−0.700100	−	1.21261i	−0.968431	−	0.249282i	$-0.919805\pi$
$709$	−6.64388e9	−	1.15075e10i	−0.700100	−	1.21261i	0.268331	−	0.963327i	$-0.413528\pi$
$710$	1.61375e10	+	2.69349e9i	1.69212	+	0.282430i
$711$	−6.26304e9			−0.653494
$712$	−1.64362e10	+	4.51228e8i	−1.70656	+	0.0468507i
$713$	5.10131e6	−	2.94524e6i	0.000527070	−	0.000304304i
$714$	2.61948e9	−	1.56941e10i	0.269322	−	1.61359i
$715$	1.31352e10			1.34389
$716$	−3.08032e9	−	1.57758e10i	−0.313618	−	1.60618i
$717$	−1.04772e10	−	6.04903e9i	−1.06152	−	0.612871i
$718$	5.97225e9	−	2.23581e9i	0.602147	−	0.225423i
$719$	−6.18260e9	−	3.56953e9i	−0.620326	−	0.358145i	0.156670	−	0.987651i	$-0.449924\pi$
$719$	−6.18260e9	−	3.56953e9i	−0.620326	−	0.358145i	−0.776996	+	0.629506i	$0.783257\pi$
$720$	−5.19143e9	+	2.10768e9i	−0.518350	+	0.210446i
$721$			2.30731e10i			2.29262i
$722$	8.37665e9	+	5.66609e9i	0.828305	+	0.560277i
$723$		−	1.32168e10i		−	1.30060i
$724$	9.17727e9	+	1.05393e10i	0.898729	+	1.03211i
$725$	−1.46399e10	−	8.45236e9i	−1.42678	−	0.823749i
$726$	−5.57861e9	−	1.49015e10i	−0.541063	−	1.44528i
$727$	−9.80907e9	−	5.66327e9i	−0.946798	−	0.546634i	−0.0547131	−	0.998502i	$-0.517424\pi$
$727$	−9.80907e9	−	5.66327e9i	−0.946798	−	0.546634i	−0.892085	+	0.451868i	$0.850758\pi$
$728$	2.27341e8	+	8.28100e9i	0.0218383	+	0.795468i
$729$	3.83663e9			0.366778
$730$	−2.47371e10	−	4.12884e9i	−2.35353	−	0.392824i
$731$	1.38121e10	−	7.97440e9i	1.30782	−	0.755070i
$732$	−1.36222e9	−	6.97653e9i	−0.128368	−	0.657432i
$733$	−1.02295e10			−0.959379			−0.479689	−	0.877438i	$-0.659251\pi$
$733$	−1.02295e10			−0.959379			−0.479689	+	0.877438i	$0.659251\pi$
$734$	9.90007e8	−	5.93143e9i	0.0924064	−	0.553635i
$735$	−6.13576e9	−	1.06274e10i	−0.569984	−	0.987241i
$736$	−1.67569e7	−	7.48374e7i	−0.00154925	−	0.00691905i
$737$	−8.32718e9	+	4.80770e9i	−0.766235	+	0.442386i
$738$	9.50336e7	+	7.82723e7i	0.00870322	+	0.00716821i
$739$	3.88629e9	+	2.24375e9i	0.354226	+	0.204512i	0.666545	−	0.745465i	$-0.267773\pi$
$739$	3.88629e9	+	2.24375e9i	0.354226	+	0.204512i	−0.312319	+	0.949977i	$0.601106\pi$
$740$	−3.95714e8	+	1.15240e9i	−0.0358980	+	0.104542i
$741$	5.94045e9	+	5.40532e9i	0.536359	+	0.488042i
$742$	1.29396e10	+	2.15974e9i	1.16281	+	0.194083i
$743$	−7.75119e9	+	1.34255e10i	−0.693278	+	1.20079i	0.277479	+	0.960732i	$0.410501\pi$
$743$	−7.75119e9	+	1.34255e10i	−0.693278	+	1.20079i	−0.970758	+	0.240062i	$0.922832\pi$
$744$	9.68246e8	−	5.95030e8i	0.0861947	−	0.0529705i
$745$	−1.11518e10	−	1.93155e10i	−0.988092	−	1.71143i
$746$	9.39549e9	+	7.73838e9i	0.828578	+	0.682440i
$747$	−3.38117e8	+	1.95212e8i	−0.0296787	+	0.0171350i
$748$	6.06200e9	−	1.76537e10i	0.529615	−	1.54234i
$749$		−	1.55467e10i		−	1.35193i
$750$	4.53161e8	+	1.21048e9i	0.0392228	+	0.104771i
$751$	1.71854e9	+	2.97660e9i	0.148054	+	0.256437i	0.930508	−	0.366271i	$-0.119366\pi$
$751$	1.71854e9	+	2.97660e9i	0.148054	+	0.256437i	−0.782454	+	0.622708i	$0.786032\pi$
$752$	−7.00905e9	+	9.00247e9i	−0.601031	+	0.771968i
$753$			8.58618e9i			0.732854i
$754$	−3.92394e9	−	1.04816e10i	−0.333367	−	0.890485i
$755$	−8.41888e9	+	1.45819e10i	−0.711934	+	1.23311i
$756$	−1.08570e10	+	2.11990e9i	−0.913867	+	0.178439i
$757$	−9.33921e9	+	1.61760e10i	−0.782482	+	1.35530i	0.148010	+	0.988986i	$0.452713\pi$
$757$	−9.33921e9	+	1.61760e10i	−0.782482	+	1.35530i	−0.930492	+	0.366313i	$0.880620\pi$
$758$	−1.26804e10	+	1.53958e10i	−1.05753	+	1.28399i
$759$	1.52983e8			0.0126998
$760$	−3.23767e9	+	1.70907e10i	−0.267538	+	1.41225i
$761$	7.68134e9			0.631816			0.315908	−	0.948790i	$-0.397691\pi$
$761$	7.68134e9			0.631816			0.315908	+	0.948790i	$0.397691\pi$
$762$	−4.58047e9	+	5.56134e9i	−0.375031	+	0.455341i
$763$	−1.38887e10	+	2.40560e10i	−1.13195	+	1.96059i
$764$	5.75341e9	−	1.12339e9i	0.466765	−	0.0911390i
$765$	3.71690e9	−	6.43786e9i	0.300169	−	0.519908i
$766$	6.15065e9	+	1.64295e10i	0.494448	+	1.32076i
$767$		−	7.10478e8i		−	0.0568547i
$768$	−3.62798e9	−	1.43445e10i	−0.289002	−	1.14267i
$769$	1.85258e9	+	3.20876e9i	0.146904	+	0.254446i	0.930082	−	0.367352i	$-0.119736\pi$
$769$	1.85258e9	+	3.20876e9i	0.146904	+	0.254446i	−0.783177	+	0.621798i	$0.786402\pi$
$770$	−1.25481e10	−	3.35182e10i	−0.990512	−	2.64584i
$771$		−	9.67390e9i		−	0.760171i
$772$	−1.60892e9	+	4.68549e9i	−0.125856	+	0.366518i
$773$	2.67276e9	−	1.54312e9i	0.208128	−	0.120163i	−0.392313	−	0.919832i	$-0.628325\pi$
$773$	2.67276e9	−	1.54312e9i	0.208128	−	0.120163i	0.600441	+	0.799669i	$0.294992\pi$
$774$	5.45394e9	+	4.49202e9i	0.422783	+	0.348216i
$775$	−5.92878e8	−	1.02690e9i	−0.0457519	−	0.0792447i
$776$	2.14163e9	+	3.48491e9i	0.164524	+	0.267717i
$777$	7.66455e8	−	1.32754e9i	0.0586156	−	0.101525i
$778$	−8.52818e9	−	1.42343e9i	−0.649274	−	0.108369i
$779$	3.64130e8	−	1.16212e8i	0.0275978	−	0.00880782i
$780$	−4.48656e9	+	1.30657e10i	−0.338518	+	0.985831i
$781$	−2.09113e10	−	1.20732e10i	−1.57073	−	0.906864i
$782$	7.85402e7	+	6.46879e7i	0.00587311	+	0.00483726i
$783$	1.29427e10	−	7.47249e9i	0.963518	−	0.556287i
$784$	8.41230e9	−	3.41532e9i	0.623460	−	0.253120i
$785$	1.90626e10	+	3.30174e10i	1.40650	+	2.43613i
$786$	−1.84405e9	+	1.10483e10i	−0.135455	+	0.811551i
$787$	7.85050e9			0.574098			0.287049	−	0.957916i	$-0.407326\pi$
$787$	7.85050e9			0.574098			0.287049	+	0.957916i	$0.407326\pi$
$788$	2.68003e9	+	1.37257e10i	0.195118	+	0.999292i
$789$	2.13281e10	−	1.23138e10i	1.54591	−	0.892530i
$790$	−3.29878e10	−	5.50595e9i	−2.38045	−	0.397317i
$791$	2.89597e9			0.208054
$792$	8.26614e9	−	2.26933e8i	0.591241	−	0.0162315i
$793$	−4.25238e9	−	2.45511e9i	−0.302814	−	0.174830i
$794$	−5.75381e9	−	1.53695e10i	−0.407929	−	1.08965i
$795$	1.89457e10	+	1.09383e10i	1.33729	+	0.772084i
$796$	−4.54716e9	−	5.22199e9i	−0.319554	−	0.366979i
$797$			5.46820e9i			0.382596i	0.981532	+	0.191298i	$0.0612696\pi$
$797$			5.46820e9i			0.382596i	−0.981532	+	0.191298i	$0.938730\pi$
$798$	8.11829e9	−	2.03225e10i	0.565529	−	1.41569i
$799$		−	1.51374e10i		−	1.04987i
$800$	−1.50648e10	+	3.37316e9i	−1.04028	+	0.232928i
$801$	8.36979e9	+	4.83230e9i	0.575441	+	0.332231i
$802$	1.52814e10	−	5.72084e9i	1.04605	−	0.391606i
$803$	3.20549e10	+	1.85069e10i	2.18469	+	1.26133i
$804$	−1.93798e9	−	9.92531e9i	−0.131508	−	0.673516i
$805$	1.95099e8			0.0131817
$806$	1.29243e8	−	7.74333e8i	0.00869429	−	0.0520901i
$807$	−2.76252e10	+	1.59494e10i	−1.85032	+	1.06828i
$808$	1.12487e8	+	4.09737e9i	0.00750172	+	0.273253i
$809$	1.68979e10			1.12205			0.561026	−	0.827798i	$-0.310407\pi$
$809$	1.68979e10			1.12205			0.561026	+	0.827798i	$0.310407\pi$
$810$	−2.65414e10	−	4.42999e9i	−1.75480	−	0.292891i
$811$	−9.13958e9	−	1.58302e10i	−0.601663	−	1.04211i	−0.992569	−	0.121680i	$-0.961172\pi$
$811$	−9.13958e9	−	1.58302e10i	−0.601663	−	1.04211i	0.390907	−	0.920430i	$-0.372162\pi$
$812$	−2.29982e10	+	2.00261e10i	−1.50747	+	1.31266i
$813$	−1.06643e10	+	6.15706e9i	−0.696012	+	0.401843i
$814$	1.14325e9	−	1.38807e9i	0.0742945	−	0.0902040i
$815$	−2.02485e10	−	1.16905e10i	−1.31021	−	0.756450i
$816$	1.54898e10	+	1.20599e10i	0.998000	+	0.777012i
$817$	2.08973e10	−	6.66934e9i	1.34064	−	0.427864i
$818$	−1.51770e9	+	9.09302e9i	−0.0969505	+	0.580860i
$819$	2.43464e9	−	4.21693e9i	0.154861	−	0.268227i
$820$	4.31737e8	+	4.95810e8i	0.0273445	+	0.0314027i
$821$	3.60384e9	+	6.24203e9i	0.227282	+	0.393663i	0.957002	−	0.290083i	$-0.0936829\pi$
$821$	3.60384e9	+	6.24203e9i	0.227282	+	0.393663i	−0.729720	+	0.683746i	$0.760350\pi$
$822$	−1.80175e10	+	2.18758e10i	−1.13147	+	1.37376i
$823$	−1.09327e10	+	6.31198e9i	−0.683639	+	0.394699i	−0.801225	−	0.598363i	$-0.795818\pi$
$823$	−1.09327e10	+	6.31198e9i	−0.683639	+	0.394699i	0.117586	+	0.993063i	$0.462485\pi$
$824$	−2.50346e10	−	1.35517e10i	−1.55882	−	0.843816i
$825$		−	3.07955e10i		−	1.90941i
$826$	−1.81299e9	+	6.78721e8i	−0.111935	+	0.0419045i
$827$	−2.40607e8	−	4.16744e8i	−0.0147924	−	0.0256212i	0.858534	−	0.512756i	$-0.171375\pi$
$827$	−2.40607e8	−	4.16744e8i	−0.0147924	−	0.0256212i	−0.873327	+	0.487135i	$0.838042\pi$
$828$	−1.46398e7	+	4.26341e7i	−0.000896251	+	0.00261006i
$829$		−	1.03620e10i		−	0.631685i	−0.948812	−	0.315843i	$-0.897713\pi$
$829$		−	1.03620e10i		−	0.631685i	0.948812	−	0.315843i	$-0.102287\pi$
$830$	−1.95250e9	+	7.30949e8i	−0.118527	+	0.0443725i
$831$	7.54007e9	−	1.30598e10i	0.455797	−	0.789464i
$832$	−9.11853e9	−	4.61707e9i	−0.548900	−	0.277929i
$833$	−6.02295e9	+	1.04321e10i	−0.361037	+	0.625334i
$834$	2.13609e10	+	1.75934e10i	1.27508	+	1.05019i
$835$	−3.19936e8			−0.0190178
$836$	1.33186e10	−	2.19473e10i	0.788380	−	1.29915i
$837$	1.04829e9			0.0617936
$838$	−4.87527e9	−	4.01540e9i	−0.286183	−	0.235708i
$839$	8.93788e9	−	1.54809e10i	0.522478	−	0.904958i	−0.477180	−	0.878805i	$-0.658341\pi$
$839$	8.93788e9	−	1.54809e10i	0.522478	−	0.904958i	0.999658	−	0.0261524i	$-0.00832552\pi$
$840$	3.76270e10	−	1.03299e9i	2.19039	−	0.0601336i
$841$	1.19749e10	−	2.07411e10i	0.694202	−	1.20239i
$842$	−1.00456e10	+	3.76073e9i	−0.579941	+	0.217110i
$843$		−	2.51407e10i		−	1.44538i
$844$	6.11178e9	+	2.09868e9i	0.349920	+	0.120157i
$845$	−7.83345e9	−	1.35679e10i	−0.446637	−	0.773598i
$846$	6.28052e9	−	2.35121e9i	0.356615	−	0.133504i
$847$			2.99483e10i			1.69348i
$848$	−9.94327e9	+	1.27712e10i	−0.559943	+	0.719194i
$849$	−1.07035e10	+	6.17968e9i	−0.600275	+	0.346569i
$850$	1.30217e10	−	1.58102e10i	0.727279	−	0.883020i
$851$	4.90138e6	+	8.48944e6i	0.000272625	+	0.000472200i
$852$	1.91519e10	−	1.66769e10i	1.06090	−	0.923800i
$853$	−7.24782e9	+	1.25536e10i	−0.399840	+	0.692543i	−0.993706	−	0.112021i	$-0.964268\pi$
$853$	−7.24782e9	+	1.25536e10i	−0.399840	+	0.692543i	0.593866	+	0.804564i	$0.297601\pi$
$854$	−2.20262e9	+	1.31965e10i	−0.121014	+	0.725033i
$855$	6.88106e9	−	7.56229e9i	0.376508	−	0.413783i
$856$	1.68684e10	+	9.13117e9i	0.919214	+	0.497586i
$857$	1.36116e10	+	7.85864e9i	0.738712	+	0.426496i	0.821601	−	0.570063i	$-0.193081\pi$
$857$	1.36116e10	+	7.85864e9i	0.738712	+	0.426496i	−0.0828885	+	0.996559i	$0.526415\pi$
$858$	1.29621e10	−	1.57378e10i	0.700597	−	0.850624i
$859$	6.62627e9	−	3.82568e9i	0.356692	−	0.205936i	−0.310937	−	0.950431i	$-0.600643\pi$
$859$	6.62627e9	−	3.82568e9i	0.356692	−	0.205936i	0.667629	+	0.744495i	$0.267309\pi$
$860$	2.47772e10	+	2.84544e10i	1.32834	+	1.52547i
$861$	−4.13557e8	−	7.16302e8i	−0.0220813	−	0.0382459i
$862$	1.01858e9	+	1.70010e8i	0.0541653	+	0.00904066i
$863$	−1.04617e10			−0.554072			−0.277036	−	0.960859i	$-0.589352\pi$
$863$	−1.04617e10			−0.554072			−0.277036	+	0.960859i	$0.589352\pi$
$864$	4.07659e9	−	1.30251e10i	0.215030	−	0.687041i
$865$	1.18383e9	−	6.83484e8i	0.0621918	−	0.0359064i
$866$	−3.92167e9	+	2.34959e10i	−0.205191	+	1.22936i
$867$	−3.42781e9			−0.178628
$868$	−2.09940e9	+	4.09922e8i	−0.108962	+	0.0212756i
$869$	4.27463e10	+	2.46796e10i	2.20968	+	1.27576i
$870$	−4.76259e10	+	1.78295e10i	−2.45203	+	0.917957i
$871$	−6.04973e9	−	3.49282e9i	−0.310222	−	0.179107i
$872$	−1.79438e10	−	2.91985e10i	−0.916443	−	1.49126i
$873$		−	2.40426e9i		−	0.122302i
$874$	8.65907e7	+	1.09940e8i	0.00438714	+	0.00557013i
$875$		−	2.43276e9i		−	0.122764i
$876$	−2.93580e10	+	2.55641e10i	−1.47558	+	1.28489i
$877$	1.25989e10	+	7.27400e9i	0.630718	+	0.364145i	0.781030	−	0.624493i	$-0.214694\pi$
$877$	1.25989e10	+	7.27400e9i	0.630718	+	0.364145i	−0.150312	+	0.988639i	$0.548028\pi$
$878$	−5.95862e7	−	1.59166e8i	−0.00297109	−	0.00793631i
$879$	−1.04628e10	−	6.04069e9i	−0.519620	−	0.300003i
$880$	4.37377e10	+	6.07163e9i	2.16355	+	0.300342i
$881$	−3.81210e10			−1.87823			−0.939114	−	0.343605i	$-0.888352\pi$
$881$	−3.81210e10			−1.87823			−0.939114	+	0.343605i	$0.888352\pi$
$882$	−5.26379e9	−	8.78571e8i	−0.258320	−	0.0431159i
$883$	9.86470e9	−	5.69539e9i	0.482193	−	0.278395i	−0.239137	−	0.970986i	$-0.576864\pi$
$883$	9.86470e9	−	5.69539e9i	0.482193	−	0.278395i	0.721330	+	0.692591i	$0.243531\pi$
$884$	1.33093e10	−	2.59872e9i	0.647994	−	0.126525i
$885$	−3.22825e9			−0.156555
$886$	−1.90433e9	+	1.14094e10i	−0.0919865	+	0.551119i
$887$	1.02177e10	+	1.76976e10i	0.491611	+	0.851495i	0.999953	−	0.00965979i	$-0.00307486\pi$
$887$	1.02177e10	+	1.76976e10i	0.491611	+	0.851495i	−0.508342	+	0.861155i	$0.669742\pi$
$888$	9.90232e8	+	1.61133e9i	0.0474561	+	0.0772216i
$889$	1.17440e10	−	6.78039e9i	0.560608	−	0.323667i
$890$	3.98360e10	+	3.28100e10i	1.89413	+	1.56006i
$891$	3.43930e10	+	1.98568e10i	1.62891	+	0.940453i
$892$	3.35188e10	+	1.15098e10i	1.58129	+	0.542989i
$893$	4.43509e9	−	2.03419e10i	0.208412	−	0.955896i
$894$	−3.41474e10	−	5.69949e9i	−1.59837	−	0.266781i
$895$	−2.52254e10	+	4.36918e10i	−1.17614	+	2.03713i
$896$	−3.07082e9	+	2.76793e10i	−0.142619	+	1.28551i
$897$	5.55713e7	+	9.62523e7i	0.00257085	+	0.00445284i
$898$	−8.54348e9	−	7.03664e9i	−0.393702	−	0.324264i
$899$	2.50272e9	−	1.44494e9i	0.114882	−	0.0663273i
$900$	8.58226e9	+	2.94700e9i	0.392421	+	0.134751i
$901$		−	2.14744e10i		−	0.978102i
$902$	−3.40188e8	−	9.08703e8i	−0.0154346	−	0.0412287i
$903$	−2.37339e10	−	4.11083e10i	−1.07266	−	1.85790i
$904$	−1.70091e9	+	3.14217e9i	−0.0765759	+	0.141462i
$905$		−	4.38635e10i		−	1.96713i
$906$	9.16325e9	+	2.44767e10i	0.409355	+	1.09346i
$907$	1.37168e10	−	2.37582e10i	0.610418	−	1.05728i	−0.380751	−	0.924677i	$-0.624335\pi$
$907$	1.37168e10	−	2.37582e10i	0.610418	−	1.05728i	0.991170	−	0.132598i	$-0.0423320\pi$
$908$	4.26433e8	+	2.18396e9i	0.0189039	+	0.0968155i
$909$	1.20464e9	−	2.08650e9i	0.0531966	−	0.0921393i
$910$	1.65306e10	−	2.00705e10i	0.727182	−	0.882902i
$911$	1.56766e10			0.686971			0.343485	−	0.939158i	$-0.388392\pi$
$911$	1.56766e10			0.686971			0.343485	+	0.939158i	$0.388392\pi$
$912$	1.72820e10	+	2.07446e10i	0.754419	+	0.905573i
$913$	3.07695e9			0.133805
$914$	2.80537e10	−	3.40611e10i	1.21529	−	1.47553i
$915$	−1.11555e10	+	1.93219e10i	−0.481409	+	0.833826i
$916$	1.10255e9	+	5.64667e9i	0.0473985	+	0.242750i
$917$	1.05413e10	−	1.82581e10i	0.451441	−	0.781919i
$918$	6.34866e9	+	1.69584e10i	0.270852	+	0.723496i
$919$			2.55998e10i			1.08801i	0.839083	+	0.544004i	$0.183092\pi$
$919$			2.55998e10i			1.08801i	−0.839083	+	0.544004i	$0.816908\pi$
$920$	−1.14589e8	+	2.11686e8i	−0.00485161	+	0.00896261i
$921$	−7.75014e9	−	1.34236e10i	−0.326889	−	0.566189i
$922$	1.53370e9	+	4.09679e9i	0.0644439	+	0.172141i
$923$		−	1.75424e10i		−	0.734316i
$924$	−5.25421e10	−	1.80421e10i	−2.19107	−	0.752376i
$925$	1.70893e9	−	9.86651e8i	0.0709950	−	0.0409890i
$926$	−3.35414e10	−	2.76256e10i	−1.38817	−	1.14334i
$927$	8.36631e9	+	1.44909e10i	0.344949	+	0.597469i
$928$	−8.22097e9	−	3.67155e10i	−0.337680	−	1.50810i
$929$	−1.44620e10	+	2.50489e10i	−0.591797	+	1.02502i	0.402193	+	0.915555i	$0.368248\pi$
$929$	−1.44620e10	+	2.50489e10i	−0.591797	+	1.02502i	−0.993990	+	0.109468i	$0.965085\pi$
$930$	−3.51840e9	−	5.87251e8i	−0.143435	−	0.0239405i
$931$	−1.11502e10	+	1.22541e10i	−0.452855	+	0.497688i
$932$	−2.17380e10	−	7.46448e9i	−0.879558	−	0.302026i
$933$	−7.23621e9	−	4.17783e9i	−0.291692	−	0.168409i
$934$	1.09609e10	+	9.02771e9i	0.440182	+	0.362546i
$935$	−5.07370e10	+	2.92930e10i	−2.02994	+	1.17199i
$936$	3.14547e9	+	5.11838e9i	0.125378	+	0.204017i
$937$	−4.64662e9	−	8.04818e9i	−0.184522	−	0.319602i	0.758893	−	0.651215i	$-0.225740\pi$
$937$	−4.64662e9	−	8.04818e9i	−0.184522	−	0.319602i	−0.943415	+	0.331613i	$0.892407\pi$
$938$	−3.13360e9	+	1.87743e10i	−0.123975	+	0.742770i
$939$	1.66482e10			0.656204
$940$	3.51469e10	−	6.86266e9i	1.38019	−	0.269491i
$941$	−1.83772e10	+	1.06101e10i	−0.718979	+	0.415103i	−0.814377	−	0.580337i	$-0.802921\pi$
$941$	−1.83772e10	+	1.06101e10i	−0.718979	+	0.415103i	0.0953979	+	0.995439i	$0.469588\pi$
$942$	5.83708e10	+	9.74259e9i	2.27519	+	0.379749i
$943$	5.28929e6			0.000205403
$944$	3.28413e8	−	2.36576e9i	0.0127063	−	0.0915310i
$945$	3.00690e10	+	1.73603e10i	1.15906	+	0.669186i
$946$	−1.95232e10	−	5.21502e10i	−0.749779	−	2.00280i
$947$	3.10161e10	+	1.79072e10i	1.18676	+	0.685175i	0.957568	−	0.288206i	$-0.0930589\pi$
$947$	3.10161e10	+	1.79072e10i	1.18676	+	0.685175i	0.229190	+	0.973382i	$0.426392\pi$
$948$	−3.91499e10	+	3.40906e10i	−1.49246	+	1.29959i
$949$			2.68907e10i			1.02134i
$950$	2.21310e10	−	1.74308e10i	0.837467	−	0.659604i
$951$		−	4.16878e10i		−	1.57173i
$952$	−1.93457e10	−	3.14798e10i	−0.726702	−	1.18251i
$953$	9.57540e9	+	5.52836e9i	0.358370	+	0.206905i	0.668365	−	0.743833i	$-0.266994\pi$
$953$	9.57540e9	+	5.52836e9i	0.358370	+	0.206905i	−0.309996	+	0.950738i	$0.600328\pi$
$954$	8.90975e9	−	3.33551e9i	0.332236	−	0.124378i
$955$	−1.59344e10	−	9.19970e9i	−0.592001	−	0.341792i
$956$	−2.75735e10	+	5.38392e9i	−1.02068	+	0.199295i
$957$	7.50538e10			2.76809
$958$	6.08703e8	−	3.64692e9i	0.0223680	−	0.134013i
$959$	4.61955e10	−	2.66710e10i	1.69135	−	0.976504i
$960$	−2.09789e10	+	4.14326e10i	−0.765304	+	1.51145i
$961$	−2.73099e10			−0.992632
$962$	1.28862e9	+	2.15082e8i	0.0466673	+	0.00778918i
$963$	−5.63725e9	−	9.76401e9i	−0.203411	−	0.352319i
$964$	−2.01554e10	−	2.31467e10i	−0.724640	−	0.832183i
$965$	1.34662e10	−	7.77469e9i	0.482390	−	0.278508i
$966$	1.92528e8	−	2.33756e8i	0.00687185	−	0.00834340i
$967$	1.08225e10	+	6.24840e9i	0.384890	+	0.222216i	0.679944	−	0.733264i	$-0.262004\pi$
$967$	1.08225e10	+	6.24840e9i	0.384890	+	0.222216i	−0.295054	+	0.955481i	$0.595338\pi$
$968$	−3.24944e10	−	1.75898e10i	−1.15145	−	0.623299i
$969$	−3.50006e10	−	7.63109e9i	−1.23578	−	0.269435i
$970$	2.11363e9	−	1.26634e10i	0.0743580	−	0.445501i
$971$	−2.10197e10	+	3.64073e10i	−0.736818	+	1.27621i	0.217104	+	0.976149i	$0.430339\pi$
$971$	−2.10197e10	+	3.64073e10i	−0.736818	+	1.27621i	−0.953921	+	0.300057i	$0.902994\pi$
$972$	−1.59551e10	+	1.38933e10i	−0.557274	+	0.485258i
$973$	−2.60432e10	−	4.51081e10i	−0.906357	−	1.56986i
$974$	9.99198e8	−	1.21317e9i	0.0346494	−	0.0420692i
$975$	1.93756e10	−	1.11865e10i	0.669483	−	0.386526i
$976$	−1.30248e10	−	1.01407e10i	−0.448431	−	0.349135i
$977$			3.62714e8i			0.0124432i	0.999981	+	0.00622162i	$0.00198042\pi$
$977$			3.62714e8i			0.0124432i	−0.999981	+	0.00622162i	$0.998020\pi$
$978$	−3.39884e10	+	1.27241e10i	−1.16183	+	0.434951i
$979$	−3.80835e10	−	6.59625e10i	−1.29717	−	2.24677i
$980$	−2.69523e10	−	9.25497e9i	−0.914754	−	0.314111i
$981$			2.01442e10i			0.681255i
$982$	3.11500e10	−	1.16615e10i	1.04971	−	0.392975i
$983$	3.58465e9	−	6.20879e9i	0.120367	−	0.208483i	−0.799545	−	0.600606i	$-0.794926\pi$
$983$	3.58465e9	−	6.20879e9i	0.120367	−	0.208483i	0.919913	+	0.392123i	$0.128259\pi$
$984$	1.02010e9	−	2.80050e7i	0.0341317	−	0.000937030i
$985$	2.19474e10	−	3.80140e10i	0.731738	−	1.26741i
$986$	3.85321e10	+	3.17361e10i	1.28013	+	1.05435i
$987$	−4.50528e10			−1.49146
$988$	1.86466e10	+	4.07262e8i	0.615106	+	0.0134346i
$989$	3.03551e8			0.00997801
$990$	−2.00344e10	−	1.65009e10i	−0.656227	−	0.540486i
$991$	2.73238e9	−	4.73262e9i	0.0891833	−	0.154470i	−0.817983	−	0.575243i	$-0.804908\pi$
$991$	2.73238e9	−	4.73262e9i	0.0891833	−	0.154470i	0.907166	+	0.420773i	$0.138241\pi$
$992$	7.88284e8	−	2.51864e9i	0.0256385	−	0.0819173i
$993$	−1.72650e9	+	2.99039e9i	−0.0559557	+	0.0969182i
$994$	−4.47645e10	+	1.67583e10i	−1.44571	+	0.541225i
$995$			2.17335e10i			0.699437i
$996$	−1.05099e9	+	3.06068e9i	−0.0337046	+	0.0981544i
$997$	1.00705e10	+	1.74426e10i	0.321824	+	0.557415i	0.980864	−	0.194692i	$-0.0623708\pi$
$997$	1.00705e10	+	1.74426e10i	0.321824	+	0.557415i	−0.659041	+	0.752107i	$0.729037\pi$
$998$	9.72729e7	−	3.64157e7i	0.00309767	−	0.00115966i
$999$			1.74454e9i			0.0553607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.f.a.27.20	✓	136
4.3	odd	2	inner	76.8.f.a.27.42	yes	136
19.12	odd	6	inner	76.8.f.a.31.42	yes	136
76.31	even	6	inner	76.8.f.a.31.20	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.f.a.27.20	✓	136	1.1	even	1	trivial
76.8.f.a.27.42	yes	136	4.3	odd	2	inner
76.8.f.a.31.20	yes	136	76.31	even	6	inner
76.8.f.a.31.42	yes	136	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.19272 + 8.73297i) q^{2} +(27.5600 - 47.7352i) q^{3} +(-24.5296 - 125.628i) q^{4} +(-200.879 + 347.932i) q^{5} +(218.640 + 584.026i) q^{6} -1173.75i q^{7} +(1273.54 + 689.387i) q^{8} +(-425.602 - 737.165i) q^{9} +O(q^{10})\)	\(q+(-7.19272 + 8.73297i) q^{2} +(27.5600 - 47.7352i) q^{3} +(-24.5296 - 125.628i) q^{4} +(-200.879 + 347.932i) q^{5} +(218.640 + 584.026i) q^{6} -1173.75i q^{7} +(1273.54 + 689.387i) q^{8} +(-425.602 - 737.165i) q^{9} +(-1593.62 - 4256.84i) q^{10} +6708.37i q^{11} +(-6672.90 - 2291.36i) q^{12} +(-4220.71 + 2436.83i) q^{13} +(10250.3 + 8442.46i) q^{14} +(11072.4 + 19178.0i) q^{15} +(-15180.6 + 6163.20i) q^{16} +(10868.8 - 18825.4i) q^{17} +(9498.88 + 1585.45i) q^{18} +(20121.4 - 22113.4i) q^{19} +(48637.4 + 16701.3i) q^{20} +(-56029.3 - 32348.5i) q^{21} +(-58584.0 - 48251.4i) q^{22} +(358.300 - 206.865i) q^{23} +(68006.7 - 41793.1i) q^{24} +(-41642.0 - 72126.0i) q^{25} +(9077.63 - 54386.8i) q^{26} +73628.9 q^{27} +(-147456. + 28791.7i) q^{28} +(175783. - 101489. i) q^{29} +(-247122. - 41246.7i) q^{30} +14237.5 q^{31} +(55366.7 - 176902. i) q^{32} +(320226. + 184882. i) q^{33} +(86225.1 + 230323. i) q^{34} +(408386. + 235781. i) q^{35} +(-82168.4 + 71549.8i) q^{36} +23693.7i q^{37} +(48388.5 + 334775. i) q^{38} +268636. i q^{39} +(-495686. + 304621. i) q^{40} +(11071.6 + 6392.21i) q^{41} +(685502. - 256628. i) q^{42} +(635397. + 366847. i) q^{43} +(842757. - 164554. i) q^{44} +341978. q^{45} +(-770.608 + 4616.95i) q^{46} +(603071. - 348183. i) q^{47} +(-124175. + 894507. i) q^{48} -554148. q^{49} +(929393. + 155124. i) q^{50} +(-599090. - 1.03765e6i) q^{51} +(409666. + 470464. i) q^{52} +(855536. - 493944. i) q^{53} +(-529592. + 642999. i) q^{54} +(-2.33406e6 - 1.34757e6i) q^{55} +(809169. - 1.49482e6i) q^{56} +(-501045. - 1.56994e6i) q^{57} +(-378063. + 2.26509e6i) q^{58} +(-72889.5 + 126248. i) q^{59} +(2.13768e6 - 1.86143e6i) q^{60} +(503751. + 872523. i) q^{61} +(-102406. + 124336. i) q^{62} +(-865248. + 499551. i) q^{63} +(1.14664e6 + 1.75592e6i) q^{64} -1.95803e6i q^{65} +(-3.91787e6 + 1.46672e6i) q^{66} +(716672. + 1.24131e6i) q^{67} +(-2.63160e6 - 903647. i) q^{68} -22804.7i q^{69} +(-4.99647e6 + 1.87051e6i) q^{70} +(-1.79971e6 + 3.11720e6i) q^{71} +(-33828.3 - 1.23221e6i) q^{72} +(2.75878e6 - 4.77834e6i) q^{73} +(-206916. - 170422. i) q^{74} -4.59060e6 q^{75} +(-3.27162e6 - 1.98536e6i) q^{76} +7.87396e6 q^{77} +(-2.34599e6 - 1.93222e6i) q^{78} +(3.67893e6 - 6.37209e6i) q^{79} +(905083. - 6.51987e6i) q^{80} +(2.96000e6 - 5.12687e6i) q^{81} +(-135458. + 50710.9i) q^{82} -458673. i q^{83} +(-2.68949e6 + 7.83232e6i) q^{84} +(4.36664e6 + 7.56324e6i) q^{85} +(-7.77389e6 + 2.91028e6i) q^{86} -1.11881e7i q^{87} +(-4.62467e6 + 8.54336e6i) q^{88} +(-9.83287e6 + 5.67701e6i) q^{89} +(-2.45975e6 + 2.98648e6i) q^{90} +(2.86023e6 + 4.95407e6i) q^{91} +(-34776.9 - 39938.1i) q^{92} +(392385. - 679631. i) q^{93} +(-1.29704e6 + 7.77098e6i) q^{94} +(3.65201e6 + 1.14430e7i) q^{95} +(-6.91855e6 - 7.51835e6i) q^{96} +(2.44613e6 + 1.41227e6i) q^{97} +(3.98583e6 - 4.83936e6i) q^{98} +(4.94518e6 - 2.85510e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Introduction

L-functions

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